类序数空间的积

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-11 DOI:10.1016/j.topol.2025.109478

Jocelyn R. Bell

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引用次数: 0

摘要

我们考虑类似于有序空间的空间和这些空间的积，特别是Σ-products和一致积：由从N到空间的所有函数集合的一致收敛的一致性所产生的拓扑。我们在这些空间上玩一个弱变异的近无穷对策，得出它们是可数近的，因此是伪正规的和α2的（在Arhangel'skii的意义上）。特别地，从我们的结果可以得出一个序空间的Σ-product是伪正规的。

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Products of ordinal-like spaces

We consider spaces that resemble ordinal spaces and products of these spaces, in particular Σ-products and uniform products: the topology generated by the uniformity of uniform convergence on the set of all functions from

N

to the space. We play a weak variation of the proximal infinite game on these spaces to conclude that they are countably proximal and so both pseudonormal and

α_{2}

(in the sense of Arhangel'skii). In particular, it follows from our results that a Σ-product of ordinal spaces is pseudonormal.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.