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Selectively pseudocompact groups and p-compactness
Topology and its Applications ( IF 0.6 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.topol.2020.107380
S. Garcia-Ferreira , A.H. Tomita

Abstract We say that a space X is selectively pseudocompact if for each sequence ( U n ) n ω of nonempty open subsets of X there is a sequence ( x n ) n ω of points in X such that x n ∈ U n , for each n ω , and the set { x n : n ω } has a cluster point in X. We prove that if p and q are not equivalent selective ultrafilters on ω, then there are a p-compact group and a q-compact group whose product is not selectively pseudocompact.

中文翻译:

选择性伪紧群和 p 紧度

摘要 如果对于 X 的非空开放子集的每个序列 ( U n ) n ω 存在 X 中点的序列 ( xn ) n ω 使得 xn ∈ U n ,对于每个 n ω,我们说空间 X 是选择性伪紧的, 并且集合 { xn : n ω } 在 X 中有一个簇点。 我们证明如果 p 和 q 不是 ω 上的等效选择性超滤子,那么存在一个 p-compact 群和一个 q-compact 群,它们的乘积不是选择性伪紧。
更新日期:2020-11-01
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