Topology and its Applications最新文献

Relatively functionally countable subsets of products 产品的相对功能可数子集

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-11-12 DOI: 10.1016/j.topol.2024.109133

Anton E. Lipin

{"title":"Relatively functionally countable subsets of products","authors":"Anton E. Lipin","doi":"10.1016/j.topol.2024.109133","DOIUrl":"10.1016/j.topol.2024.109133","url":null,"abstract":"<div><div>A subset A of a topological space X is called relatively functionally countable (RFC) in X, if for each continuous function <math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>R</mi></math> the set <math><mi>f</mi><mo>[</mo><mi>A</mi><mo>]</mo></math> is countable. We prove that all RFC subsets of a product <math><munder><mo>∏</mo><mrow><mi>n</mi><mo>∈</mo><mi>ω</mi></mrow></munder><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub></math> are countable, assuming that spaces <math><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub></math> are Tychonoff and all RFC subsets of every <math><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub></math> are countable. In particular, in a metrizable space every RFC subset is countable.</div><div>The main tool in the proof is the following result: for every Tychonoff space X and any countable set <math><mi>Q</mi><mo>⊆</mo><mi>X</mi></math> there is a continuous function <math><mi>f</mi><mo>:</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> such that the restriction of f to <math><msup><mrow><mi>Q</mi></mrow><mrow><mi>ω</mi></mrow></msup></math> is injective.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"359 ","pages":"Article 109133"},"PeriodicalIF":0.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extendability to Marczewski-Burstin countably representable ideals 扩展到马茨维斯基-布尔斯坦可数可表示理想的可扩展性

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-11-09 DOI: 10.1016/j.topol.2024.109134

Marta Kwela, Jacek Tryba

引用次数: 0

MSNR spaces revisited 重温 MSNR 空间

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-11-08 DOI: 10.1016/j.topol.2024.109132

John E. Porter

引用次数: 0

On Ψω-factorizable groups 关于Ψω可因子群

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-11-06 DOI: 10.1016/j.topol.2024.109129

Heng Zhang , Wenfei Xi , Yaoqiang Wu , Hongling Li

{"title":"On Ψω-factorizable groups","authors":"Heng Zhang , Wenfei Xi , Yaoqiang Wu , Hongling Li","doi":"10.1016/j.topol.2024.109129","DOIUrl":"10.1016/j.topol.2024.109129","url":null,"abstract":"<div><div>A topological group G is called <math><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-factorizable (resp. <math><mi>M</mi></math>-factorizable) if every continuous real-valued function on G admits a factorization via a continuous homomorphism onto a topological group H with <math><mi>ψ</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>≤</mo><mi>ω</mi></math> (resp. a first-countable group). The first purpose of this article is to discuss some characterizations of <math><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-factorizable groups. It is shown that a topological group G is <math><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-factorizable if and only if every continuous real-valued function on G is <math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi></mrow></msub></math>-uniformly continuous, if and only if for every cozero-set U of G, there exists a <math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi></mrow></msub></math>-subgroup N of G such that <math><mi>U</mi><mi>N</mi><mo>=</mo><mi>U</mi></math>. Sufficient conditions on the <math><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-factorizable group G to be <math><mi>M</mi></math>-factorizable are that G is τ-fine and τ-steady for a cardinal τ.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109129"},"PeriodicalIF":0.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the functor of comonotonically maxitive functionals 论最大单调函数的函子

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-11-05 DOI: 10.1016/j.topol.2024.109131

Taras Radul

引用次数: 0

Some remarks on (a)-characterized subgroups of the circle 关于圆的 (a) 特征子群的一些评论

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-11-05 DOI: 10.1016/j.topol.2024.109130

Nikola Bogdanovic

引用次数: 0

Frobenius identities and geometrical aspects of Joyal-Tierney Theorem 弗罗贝纽斯等式和乔亚尔-蒂尔尼定理的几何方面

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-10-31 DOI: 10.1016/j.topol.2024.109127

Jorge Picado , Aleš Pultr

引用次数: 0

Poincaré compactification for n-dimensional piecewise polynomial vector fields: Theory and applications n 维片断多项式矢量场的庞加莱压缩：理论与应用

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-10-30 DOI: 10.1016/j.topol.2024.109126

Shimin Li , Jaume Llibre , Qian Tong

{"title":"Poincaré compactification for n-dimensional piecewise polynomial vector fields: Theory and applications","authors":"Shimin Li , Jaume Llibre , Qian Tong","doi":"10.1016/j.topol.2024.109126","DOIUrl":"10.1016/j.topol.2024.109126","url":null,"abstract":"<div><div>Poincaré compactification is very important to investigate the dynamics of vector fields in the neighborhood of the infinity, which is the main concern on the escape of particles to infinity in celestial mechanics, astrophysics, astronomy and some branches of chemistry. Since then Poincaré compactification has been extended into various cases, such as: n-dimensional polynomial vector fields, Hamiltonian vector fields, quasi-homogeneous vector fields, rational vector fields, etc.</div><div>In recent years, the piecewise smooth vector fields describing situations with discontinuities such as switching, decisions, impacts etc., have been attracted more and more attention. It is worth to notice that Poincaré compactification has been extended successfully to piecewise polynomial vector fields in 2-dimensional and 3-dimensional cases, and there are also works on n-dimensional Lipschitz continuous vector fields. The main goal of present paper is to extend the Poincaré compactification to n-dimensional piecewise polynomial vector fields which are usually discontinuous, this is a missing point in the existent literature. Thus we can investigate the dynamics near the infinity of n-dimensional piecewise polynomial vector fields. As an application we study the global phase portraits for a class of 3-dimensional piecewise linear differential systems.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109126"},"PeriodicalIF":0.6,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hyperspaces of the double arrow 双箭头的超空间

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-10-29 DOI: 10.1016/j.topol.2024.109125

Sebastián Barría

引用次数: 0

A note on non-autonomous discrete dynamical systems 关于非自治离散动力系统的说明

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-10-29 DOI: 10.1016/j.topol.2024.109124

Roya Makrooni , Neda Abbasi

引用次数: 0