Compact subspaces of the space of separately continuous functions with the cross-uniform topology

被引:0
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作者
Maslyuchenko, Oleksandr [1 ,2 ]
Myronyk, Vadym [2 ]
Ivasiuk, Roman [2 ]
机构
[1] Univ Silesia Katowice, Inst Math, Bankowa 12, PL-40007 Katowice, Poland
[2] Yuriy Fedkovych Chernivtsi Natl Univ, Dept Math & Informat, Kotsiubynskoho 2, UA-58012 Chernovtsy, Ukraine
关键词
Set-open topology; Set-uniform topology; Pointwise topology; Cross-open topology; Cross-uniform topology; Separately continuous function; Space of separately continuous functions; Space of continuous functions; Eberlein compact; Rosenthal compact; Eberlein space; Compact space; Cellularity; Sharp cellularity;
D O I
10.1016/j.topol.2024.109047
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider two natural topologies on the space S(X x Y, Z) of all separately continuous functions defined on the product of two topological spaces X and Y and ranged into a topological or metric space Z. These topologies are the cross-open topology and the cross-uniform topology. We show that these topologies coincides if X and Y are pseudocompacts and Z is a metric space. We prove that a compact space K embeds into S(X x Y, Z) for infinite compacts X, Y and a metrizable space Z superset of Rif and only if the weight of K is less than the sharp cellularity of both spaces X and Y. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC license (http://creativecommons .org /licenses /by -nc /4 .0/).
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页数:11
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