可分离子集上的均匀收敛拓扑学

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-11-13 DOI:10.1016/j.topol.2024.109135

J.A. Cruz-Chapital , A.D. Rojas-Sánchez , Á. Tamariz-Mascarúa , H. Villegas-Rodríguez

引用次数: 0

摘要

对于拓扑空间 X，让 (RX)s:=(RX,Ts) 是实线 R 的 |X| 副本与 X 的可分离子集上的均匀收敛拓扑的笛卡尔积。我们确定 Cs(X) 何时密集，何时封闭于 (RX)s，并得到一些关于 Cs(X) 中 Baire 属性的结果。最后，我们确定 Cs([0,α]) 的单元性，其中 [0,α] 是属于 α+1 的序数空间，具有通常的阶拓扑。

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The uniform convergence topology on separable subsets

For a topological space X, let

{(R^{X})}_{s} : = (R^{X}, T_{s})

be the cartesian product of

| X |

copies of the real line

R

with the topology of the uniform convergence on separable subsets of X. In this article we analyze the subspace

C (X)

{(R^{X})}_{s}

of all real-valued continuous functions on X, denoted by

C_{s} (X)

. We determine when

C_{s} (X)

is dense and when is closed in

{(R^{X})}_{s}

, and we obtain some results about the Baire property in

C_{s} (X)

. Finally, we determine the cellularity of

C_{s} ([0, α])

where

[0, α]

is the space of ordinal numbers belonging to

α + 1

with its usual order topology.

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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.