Topology最新文献

{"title":"Generalized invexity in separable Hilbert spaces","authors":"Majid Soleimani-damaneh","doi":"10.1016/j.top.2009.11.004","DOIUrl":"10.1016/j.top.2009.11.004","url":null,"abstract":"<div><p>In this paper some characterizations for generalized invexity and generalized monotonicity, under separable Hilbert spaces, are provided. The results established are useful for application in many problems in pure and applied analysis.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 66-79"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local research of manifolds generated by families of self-adjoint operators","authors":"Yakov Dymarskii ,&nbsp;Olga Ivanova ,&nbsp;Eugenia Masyuta","doi":"10.1016/j.top.2009.11.021","DOIUrl":"10.1016/j.top.2009.11.021","url":null,"abstract":"<div><p>We consider V.I. Arnold’s manifold of self-adjoint operators with fixed multiplicity of eigenvalues and K. Uhlenbeck’s manifold of eigenvectors. Our aim is to consider the local analysis and the connection between these manifolds. We present the topological description of the spectrum perturbation problem, specifically the finite-multiple eigenvalue splitting problem. For investigation of manifolds, we use the local diffeomorphism introduced by D. Fujiwara, M. Tanikawa, and Sh. Yukita.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 213-223"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55189112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial ultradistributions on R+d","authors":"Oleh Lopushansky ,&nbsp;Sergii Sharyn","doi":"10.1016/j.top.2009.11.005","DOIUrl":"10.1016/j.top.2009.11.005","url":null,"abstract":"<div><p>Let <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>=</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>d</mi></mrow></msubsup><mo>)</mo></mrow></math></span> stand for Roumieu ultradistributions with supports in the positive cone <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>d</mi></mrow></msubsup></math></span>. Throughout <span><math><mi>P</mi><mrow><mo>(</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></mrow></math></span> denotes the algebra of continuous scalar polynomials on the space <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup></math></span>. We investigate the dual pair <span><math><mrow><mo>〈</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></mrow><mo>∣</mo><mi>P</mi><mrow><mo>(</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></mrow><mo>〉</mo></mrow></math></span> generated by the algebra <span><math><mi>P</mi><mrow><mo>(</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></mrow></math></span> and by its strong dual <span><math><msup><mrow><mi>P</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></mrow></math></span>. Properties of the polynomially extended operational calculus and the semigroups of shifts along the cone <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>d</mi></mrow></msubsup></math></span> are considered.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 80-90"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The diffeomorphism groups of the real line are pairwise bihomeomorphic","authors":"Taras Banakh ,&nbsp;Tatsuhiko Yagasaki","doi":"10.1016/j.top.2009.11.010","DOIUrl":"10.1016/j.top.2009.11.010","url":null,"abstract":"<div><p>For an <span><math><mi>r</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>∞</mi></math></span>, by <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math></span>, <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>r</mi></mrow></msubsup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math></span>, <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math></span> we denote respectively the groups of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> diffeomorphisms, orientation-preserving <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> diffeomorphisms, and compactly supported <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> diffeomorphisms of the real line. We think of these groups as bitopologies spaces endowed with the compact-open <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> topology and the Whitney <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> topology. We prove that all the triples <span><math><mrow><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>,</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>r</mi></mrow></msubsup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>,</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span>, <span><math><mn>0</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mi>∞</mi></math></span>, are pairwise bitopologically equivalent, which allows us to apply known results on the topological structure of homeomorphism groups of the real line to recognizing the topological structure of the diffeomorphism groups of <span><math><mi>R</mi></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 119-129"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Free Banach spaces and extension of Lipschitz maps","authors":"M. Dubei ,&nbsp;E.D. Tymchatyn ,&nbsp;A. Zagorodnyuk","doi":"10.1016/j.top.2009.11.020","DOIUrl":"10.1016/j.top.2009.11.020","url":null,"abstract":"<div><p>Let <span><math><mi>X</mi></math></span> be a metric space. We study the free Banach space <span><math><mi>B</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> over <span><math><mi>X</mi></math></span>, that is a predual space of the Banach space of all Lipschitz functions on <span><math><mi>X</mi></math></span> which preserve a marked point <span><math><mi>θ</mi><mo>∈</mo><mi>X</mi></math></span>. Some applications to the extension theory of Lipschitz and two-Lipschitz functions are obtained.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 203-212"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55189099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Publication information","authors":"","doi":"10.1016/S0040-9383(10)00004-2","DOIUrl":"https://doi.org/10.1016/S0040-9383(10)00004-2","url":null,"abstract":"","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Page IFC"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0040-9383(10)00004-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138301609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpolating sequences on uniform algebras","authors":"Pablo Galindo ,&nbsp;Mikael Lindström ,&nbsp;Alejandro Miralles","doi":"10.1016/j.top.2009.11.009","DOIUrl":"10.1016/j.top.2009.11.009","url":null,"abstract":"<div><p>We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, then it is sufficient for any dual uniform algebra.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 111-118"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The topology of systems of hyperspaces determined by dimension functions","authors":"Taras Banakh ,&nbsp;Natalia Mazurenko","doi":"10.1016/j.top.2009.11.002","DOIUrl":"10.1016/j.top.2009.11.002","url":null,"abstract":"<div><p>Given a non-degenerate Peano continuum <span><math><mi>X</mi></math></span>, a dimension function <span><math><mstyle><mi>D</mi></mstyle><mo>:</mo><msubsup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow><mrow><mi>X</mi></mrow></msubsup><mo>→</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>]</mo></mrow></math></span> defined on the family <span><math><msubsup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow><mrow><mi>X</mi></mrow></msubsup></math></span> of compact subsets of <span><math><mi>X</mi></math></span>, and a subset <span><math><mi>Γ</mi><mo>⊂</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span>, we recognize the topological structure of the system <span><math><msub><mrow><mrow><mo>〈</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>X</mi></mrow></msup><mo>,</mo><msub><mrow><mstyle><mi>D</mi></mstyle></mrow><mrow><mo>≤</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>〉</mo></mrow></mrow><mrow><mi>α</mi><mo>∈</mo><mi>Γ</mi></mrow></msub></math></span>, where <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>X</mi></mrow></msup></math></span> is the hyperspace of non-empty compact subsets of <span><math><mi>X</mi></math></span> and <span><math><msub><mrow><mstyle><mi>D</mi></mstyle></mrow><mrow><mo>≤</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> is the subspace of <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>X</mi></mrow></msup></math></span>, consisting of non-empty compact subsets <span><math><mi>K</mi><mo>⊂</mo><mi>X</mi></math></span> with <span><math><mstyle><mi>D</mi></mstyle><mrow><mo>(</mo><mi>K</mi><mo>)</mo></mrow><mo>≤</mo><mi>γ</mi></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 43-53"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The spectra of algebras of Lorch analytic mappings","authors":"Luiza A. Moraes,&nbsp;Alex F. Pereira","doi":"10.1016/j.top.2009.11.006","DOIUrl":"10.1016/j.top.2009.11.006","url":null,"abstract":"<div><p>For a complex Banach algebra <span><math><mi>E</mi></math></span>, let <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>L</mi></mrow></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></math></span> be the space of the mappings from <span><math><mi>E</mi></math></span> into <span><math><mi>E</mi></math></span> that are analytic in the sense of Lorch. We will show that <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>L</mi></mrow></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></math></span> is a closed subalgebra of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>E</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></math></span> and we will give a description of its spectrum. As an application we will show that <span><math><mi>E</mi></math></span> is semi-simple if and only if <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>L</mi></mrow></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></math></span> is semi-simple. We will also give descriptions of the spectra of other algebras of analytic mappings in the sense of Lorch. In particular we will study the spectrum of the Banach algebra <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msubsup><mrow><mo>(</mo><mstyle><mi>int</mi></mstyle><mspace></mspace><msub><mrow><mi>B</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo></mrow></math></span> of the bounded mappings from <span><math><mstyle><mi>int</mi></mstyle><mspace></mspace><msub><mrow><mi>B</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> into <span><math><mi>E</mi></math></span> that are analytic in the sense of Lorch.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 91-99"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Sugeno integral and functional representation of the monad of lattice-valued capacities","authors":"O.R. Nykyforchyn","doi":"10.1016/j.top.2009.11.012","DOIUrl":"10.1016/j.top.2009.11.012","url":null,"abstract":"<div><p>The Sugeno integral of an upper semicontinuous function from a compactum to a compact Hausdorff–Lawson lattice with respect to a lattice-valued capacity is introduced, and its characterization and properties are presented. It is proved that in a family of fuzzy integrals, the Sugeno integral is unique that provides a functional representation of the monad of lattice-valued capacities.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 137-148"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}