{"title":"On dense-lineability of sets of functions on R","authors":"R.M. Aron , F.J. García-Pacheco , D. Pérez-García , J.B. Seoane-Sepúlveda","doi":"10.1016/j.top.2009.11.013","DOIUrl":"10.1016/j.top.2009.11.013","url":null,"abstract":"<div><p>A subset <span><math><mi>M</mi></math></span> of a topological vector space <span><math><mi>X</mi></math></span> is said to be dense-lineable in <span><math><mi>X</mi></math></span> if there exists an infinite dimensional linear manifold in <span><math><mi>M</mi><mo>∪</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></math></span> and dense in <span><math><mi>X</mi></math></span>. We give sufficient conditions for a lineable set to be dense-lineable, and we apply them to prove the dense-lineability of several subsets of <span><math><mi>C</mi><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></math></span>. We also develop some techniques to show that the set of differentiable nowhere monotone functions is dense-lineable in <span><math><mi>C</mi><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></math></span>. Other results related to density and dense-lineability of sets in Banach spaces are also presented.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 149-156"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188560","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}
TopologyPub Date : 2009-06-01DOI: 10.1016/j.top.2009.11.008
Andriy Lopushansky
{"title":"Sectorial operators on Wiener algebras of analytic functions","authors":"Andriy Lopushansky","doi":"10.1016/j.top.2009.11.008","DOIUrl":"10.1016/j.top.2009.11.008","url":null,"abstract":"<div><p>Quantized operators acting on approximable Wiener type algebras of analytic functions with infinitely many variables are researched. For such operators a sufficient condition of a sectorial property is established and a holomorphic calculus is constructed.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 105-110"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188971","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}
TopologyPub Date : 2009-06-01DOI: 10.1016/j.top.2009.11.015
Oleh Lopushansky
{"title":"Hardy spaces for irreducible representations of locally compact groups","authors":"Oleh Lopushansky","doi":"10.1016/j.top.2009.11.015","DOIUrl":"10.1016/j.top.2009.11.015","url":null,"abstract":"<div><p>Hardy type spaces of complex analytic functions with infinitely many variables, defined on the interior of irreducible unitary orbits of topological groups with an invariant measure are investigated. Spaces of Taylor coefficients for such classes of analytic functions are described by the associated symmetric Fock spaces.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 169-177"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55189006","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}
TopologyPub Date : 2009-06-01DOI: 10.1016/j.top.2009.11.011
Aleksandr Savchenko , Mykhailo Zarichnyi
{"title":"Fuzzy ultrametrics on the set of probability measures","authors":"Aleksandr Savchenko , Mykhailo Zarichnyi","doi":"10.1016/j.top.2009.11.011","DOIUrl":"10.1016/j.top.2009.11.011","url":null,"abstract":"<div><p>We introduce a fuzzy ultrametric on the set of probability measures with compact support defined on a fuzzy metric space. The construction is a counterpart, in the realm of fuzzy ultrametric spaces, of the construction due to Vink and Rutten of an ultrametric on the set of probability measures with compact supports on an ultrametric space.</p><p>It is proved that the set of probability measures with finite supports is dense in the natural topology generated by the defined fuzzy ultrametric.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 130-136"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188520","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}
TopologyPub Date : 2009-06-01DOI: 10.1016/j.top.2009.11.019
I. Chernega , A. Zagorodnyuk
{"title":"Generalization of the polarization formula for nonhomogeneous polynomials and analytic mappings on Banach spaces","authors":"I. Chernega , A. Zagorodnyuk","doi":"10.1016/j.top.2009.11.019","DOIUrl":"10.1016/j.top.2009.11.019","url":null,"abstract":"<div><p>We propose an analogue of the classical polarization formula for any nonhomogeneous polynomial and analytic mapping on complex Banach spaces.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 197-202"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55189073","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}
TopologyPub Date : 2009-03-01DOI: 10.1016/j.top.2009.03.002
Meirav Amram, Michael Friedman, Mina Teicher
{"title":"The fundamental group of the complement of the branch curve of the second Hirzebruch surface","authors":"Meirav Amram, Michael Friedman, Mina Teicher","doi":"10.1016/j.top.2009.03.002","DOIUrl":"10.1016/j.top.2009.03.002","url":null,"abstract":"<div><p>In this paper we prove that the Hirzebruch surface <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></msub></math></span> embedded in <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>17</mn></mrow></msup></math></span> supports the conjecture on the structure and properties of fundamental groups of complement of branch curves of generic projections, as laid out in [M. Teicher, New Invariants for surfaces, Contemp. Math. 231 (1999) 271–281]. We use the regeneration from [M. Friedman, M. Teicher, The regeneration of a 5-point, Pure and Applied Mathematics Quarterly 4 (2) (2008) 383–425. Fedor Bogomolov special issue, part I], the van Kampen theorem and properties of <span><math><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub></math></span>-groups [M. Teicher, On the quotient of the braid group by commutators of transversal half-twists and its group actions, Topology Appl. 78 (1997) 153–186], where <span><math><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub></math></span> is a quotient of the braid group <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, for <span><math><mi>n</mi><mo>=</mo><mn>16</mn></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 1","pages":"Pages 23-40"},"PeriodicalIF":0.0,"publicationDate":"2009-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.03.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188864","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}
TopologyPub Date : 2009-03-01DOI: 10.1016/j.top.2009.03.001
Bohui Chen , An-Min Li , Qi Zhang , Guosong Zhao
{"title":"Singular symplectic flops and Ruan cohomology","authors":"Bohui Chen , An-Min Li , Qi Zhang , Guosong Zhao","doi":"10.1016/j.top.2009.03.001","DOIUrl":"10.1016/j.top.2009.03.001","url":null,"abstract":"<div><p>In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient <span><span><span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>=</mo><mrow><mo>{</mo><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>∣</mo><mi>x</mi><mi>y</mi><mo>−</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></msup><mo>+</mo><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>}</mo></mrow><mo>/</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>r</mi></mrow></msub><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mo>−</mo><mi>a</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mtext>,</mtext><mspace></mspace><mi>r</mi><mo>≥</mo><mn>1</mn><mtext>,</mtext></math></span></span></span> which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let <span><math><mi>X</mi></math></span> and <span><math><mi>Y</mi></math></span> be two symplectic orbifolds connected by such a flop. We study orbifold Gromov–Witten invariants of exceptional classes on <span><math><mi>X</mi></math></span> and <span><math><mi>Y</mi></math></span> and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 1","pages":"Pages 1-22"},"PeriodicalIF":0.0,"publicationDate":"2009-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.03.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188846","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}
TopologyPub Date : 2008-11-01DOI: 10.1016/j.top.2008.05.001
Lewis Bowen , Jesús A. De Loera , Mike Develin , Francisco Santos
{"title":"Erratum to: “The Gromov norm of the product of two surfaces” [Topology 44 (2005) 321–339]","authors":"Lewis Bowen , Jesús A. De Loera , Mike Develin , Francisco Santos","doi":"10.1016/j.top.2008.05.001","DOIUrl":"10.1016/j.top.2008.05.001","url":null,"abstract":"<div><p>We report an error in the proof of Lemma 2.7 of the original article. This invalidates one direction of our main theorem.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"47 6","pages":"Pages 471-472"},"PeriodicalIF":0.0,"publicationDate":"2008-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2008.05.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188837","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}
TopologyPub Date : 2008-11-01DOI: 10.1016/j.top.2007.11.001
Marek Golasiński , Juno Mukai
{"title":"Gottlieb groups of spheres","authors":"Marek Golasiński , Juno Mukai","doi":"10.1016/j.top.2007.11.001","DOIUrl":"https://doi.org/10.1016/j.top.2007.11.001","url":null,"abstract":"<div><p>This paper takes up the systematic study of the Gottlieb groups <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>k</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></math></span> of spheres for <span><math><mi>k</mi><mo>≤</mo><mn>13</mn></math></span> by means of the classical homotopy theory methods. We fully determine the groups <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>k</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></math></span> for <span><math><mi>k</mi><mo>≤</mo><mn>13</mn></math></span> except for the 2-primary components in the cases: <span><math><mi>k</mi><mo>=</mo><mn>9</mn><mo>,</mo><mi>n</mi><mo>=</mo><mn>53</mn><mo>;</mo><mi>k</mi><mo>=</mo><mn>11</mn><mo>,</mo><mi>n</mi><mo>=</mo><mn>115</mn></math></span>. In particular, we show <span><math><mrow><mo>[</mo><msub><mrow><mi>ι</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msub><mo>]</mo></mrow><mo>=</mo><mn>0</mn></math></span> if <span><math><mi>n</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>i</mi></mrow></msup><mo>−</mo><mn>7</mn></math></span> for <span><math><mi>i</mi><mo>≥</mo><mn>4</mn></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"47 6","pages":"Pages 399-430"},"PeriodicalIF":0.0,"publicationDate":"2008-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.11.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136935278","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}