第一可数空间的维数与可数网络的巧合

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI:10.1134/S1061920824030178

I.M. Leibo

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引用次数: 0

摘要

证明了第一个可数准紧密（sigma）空间的（\( \operatorname{Ind} \）维度和（\dim\）维度的重合。这给了阿尔汉格尔斯基（A.V. Arkhangel'ski）的问题一个肯定的答案，即对于具有可数网络的第一个可数空间，维数（\operatorname{ind} X\ ）、（\( \operatorname{Ind} X\ ）和（\(\dim X\ ）是否相等。 doi 10.1134/s1061920824030178

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Coincidence of the Dimensions of First Countable Spaces with a Countable Network

The coincidence of the \( \operatorname{Ind} \) and \(\dim\) dimensions for the first countable paracompact \(\sigma\)-spaces is proved. This gives a positive answer to A.V. Arkhangel’skii’s question of whether the dimensions \( \operatorname{ind} X\), \( \operatorname{Ind} X\), and \(\dim X\) are equal for the first countable spaces with a countable network.

DOI 10.1134/S1061920824030178

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.