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Order isomorphisms between bases of topologies 拓扑基之间的序同构
Extracta Mathematicae Pub Date : 2022-06-01 DOI: 10.17398/2605-5686.37.1.139
Javier Cabello Sánchez
{"title":"Order isomorphisms between bases of topologies","authors":"Javier Cabello Sánchez","doi":"10.17398/2605-5686.37.1.139","DOIUrl":"https://doi.org/10.17398/2605-5686.37.1.139","url":null,"abstract":"In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have been able to show some results about arbitrary bases in complete metric spaces and also about regular open subsets in Hausdorff regular topological spaces.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43158889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On isolated points of the approximate point spectrum of a closed linear relation 关于闭合线性关系的近似点谱的孤立点
Extracta Mathematicae Pub Date : 2022-06-01 DOI: 10.17398/2605-5686.37.1.75
M. Lajnef, M. Mnif
{"title":"On isolated points of the approximate point spectrum of a closed linear relation","authors":"M. Lajnef, M. Mnif","doi":"10.17398/2605-5686.37.1.75","DOIUrl":"https://doi.org/10.17398/2605-5686.37.1.75","url":null,"abstract":"We investigate in this paper the isolated points of the approximate point spectrum of a closed linear relation acting on a complex Banach space by using the concepts of quasinilpotent part and the analytic core of a linear relation.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42069158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of symplectic forms induced by some tangent G-structures of higher order 高阶正切g结构诱导辛形式的表征
Extracta Mathematicae Pub Date : 2021-12-01 DOI: 10.17398/2605-5686.36.2.279
P. M. Kouotchop Wamba, G.F. Wankap Nono
{"title":"Characterization of symplectic forms induced by some tangent G-structures of higher order","authors":"P. M. Kouotchop Wamba, G.F. Wankap Nono","doi":"10.17398/2605-5686.36.2.279","DOIUrl":"https://doi.org/10.17398/2605-5686.36.2.279","url":null,"abstract":"Let (M, ω) be a symplectic manifold induced by an integrable G-structure P on M . In this paper, we characterize the symplectic manifolds induced by the tangent lifts of higher order r ≥ 1 of G-structure P, from M to TrM .","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47364097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rosenthal L∞-theorem revisited 重新审视Rosenthal L∞定理
Extracta Mathematicae Pub Date : 2021-12-01 DOI: 10.17398/2605-5686.36.2.147
L. Drewnowski
{"title":"Rosenthal L∞-theorem revisited","authors":"L. Drewnowski","doi":"10.17398/2605-5686.36.2.147","DOIUrl":"https://doi.org/10.17398/2605-5686.36.2.147","url":null,"abstract":"A remarkable Rosenthal L∞-theorem is extended to operators T : L∞(Γ, E) → F , where Γ is an infinite set, E a locally bounded (for instance, normed or p-normed) space, and F any topological vector space.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48415232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Support and separation properties of convex sets in finite dimension 有限维凸集的支持与分离性质
Extracta Mathematicae Pub Date : 2021-12-01 DOI: 10.17398/2605-5686.36.2.241
V. Soltan
{"title":"Support and separation properties of convex sets in finite dimension","authors":"V. Soltan","doi":"10.17398/2605-5686.36.2.241","DOIUrl":"https://doi.org/10.17398/2605-5686.36.2.241","url":null,"abstract":"This is a survey on support and separation properties of convex sets in the n-dimensional Euclidean space. It contains a detailed account of existing results, given either chronologically or in related groups, and exhibits them in a uniform way, including terminology and notation. We first discuss classical Minkowski’s theorems on support and separation of convex bodies, and next describe various generalizations of these results to the case of arbitrary convex sets, which concern bounding and asymptotic hyperplanes, and various types of separation by hyperplanes, slabs, and complementary convex sets.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43520152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The hitchhiker guide to Categorical Banach space theory. Part II. 范畴巴拿赫空间理论的搭便车指南。第二部分。
Extracta Mathematicae Pub Date : 2021-10-12 DOI: 10.17398/2605-5686.37.1.1
J. Castillo
{"title":"The hitchhiker guide to Categorical Banach space theory. Part II.","authors":"J. Castillo","doi":"10.17398/2605-5686.37.1.1","DOIUrl":"https://doi.org/10.17398/2605-5686.37.1.1","url":null,"abstract":"What has category theory to offer to Banach spacers? In this second part survey-like paper we will focus on very much needed advanced categorical and homological elements, such as Kan extensions, derived category and derived functor or Abelian hearts of Banach spaces.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46868031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Cone asymptotes of convex sets 凸集的圆锥渐近线
Extracta Mathematicae Pub Date : 2021-06-20 DOI: 10.17398/2605-5686.36.1.81
V. Soltan
{"title":"Cone asymptotes of convex sets","authors":"V. Soltan","doi":"10.17398/2605-5686.36.1.81","DOIUrl":"https://doi.org/10.17398/2605-5686.36.1.81","url":null,"abstract":"Based on the notion of plane asymptote, we introduce the new concept of cone asymptote of a set in the n-dimensional Euclidean space. We discuss the existence and describe some families of cone asymptotes.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45755858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of some essential B-spectra of pencil operators and application 铅笔算子若干基本b谱的稳定性及其应用
Extracta Mathematicae Pub Date : 2021-06-20 DOI: 10.17398/2605-5686.36.1.63
A. Ben Ali, M. Boudhief, N. Moalla
{"title":"Stability of some essential B-spectra of pencil operators and application","authors":"A. Ben Ali, M. Boudhief, N. Moalla","doi":"10.17398/2605-5686.36.1.63","DOIUrl":"https://doi.org/10.17398/2605-5686.36.1.63","url":null,"abstract":"In this paper, we give some results on the essential B-spectra of a linear operator pencil, which are used to determine the essential B-spectra of an integro-differential operator with abstract boundary conditions in the Banach space Lp([−a, a] × [−1, 1]), p ≥ 1 and a > 0.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45367636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Homotopy theory of Moore flows (II) 摩尔流的同调理论（Ⅱ）
Extracta Mathematicae Pub Date : 2021-02-15 DOI: 10.17398/2605-5686.36.2.157
P. Gaucher
{"title":"Homotopy theory of Moore flows (II)","authors":"P. Gaucher","doi":"10.17398/2605-5686.36.2.157","DOIUrl":"https://doi.org/10.17398/2605-5686.36.2.157","url":null,"abstract":"This paper proves that the q-model structures of Moore flows and of multipointed d-spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed d-spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a left adjoint nor a right adjoint. It is even possible to write an inverse up to homotopy of this functor using Moore flows.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47657145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Free (rational) derivation 自由(有理)推导
Extracta Mathematicae Pub Date : 2020-12-14 DOI: 10.17398/2605-5686.36.1.25
Konrad Schrempf
{"title":"Free (rational) derivation","authors":"Konrad Schrempf","doi":"10.17398/2605-5686.36.1.25","DOIUrl":"https://doi.org/10.17398/2605-5686.36.1.25","url":null,"abstract":"By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer’s linear representations, we provide an algorithmic construction for the (partial) non-commutative (or Hausdorff-) derivative and show how it can be applied to the non-commutative version of the Newton iteration to find roots of matrix-valued rational equations.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41588695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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