A compact space K is Corson compact if and only if Cp(K) has a dense lc-scattered subspace

被引：3

作者：

Tkachuk, V. V. ^{[1
]}

机构：

[1] Univ Autonoma Metropolitana, Dept Matemat, Ave San Rafael Atlixco,186,Col Vicentina,Mex DF, Mexico City 09340, Mexico

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 533卷 / 01期

关键词：

Scattered space; Lindel & ouml; f space; lc-scattered space; Corson compact space; Zero-dimensional space; Functionally countable space;

D O I：

10.1016/j.jmaa.2023.127992

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish that a compact space K is Corson compact if and only if it can be embedded in a topological group which is a W-space in the sense of Gruenhage. As a application of this result we show that K is Corson compact if and only if it embeds in Cp(X) for a Lindel & ouml;f scattered space X. We also prove that a zero-dimensional compact space K is Corson if and only if Cp(K, {0, 1}) is a continuous image of a Lindel & ouml;f scattered space. Besides, a zero-dimensional countably compact space Xis omega-monolithic if and only if Cp(X) has a dense functionally countable subspace. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：11

共 24 条

[21] Compact K-Band Current Mode Tunable Active Only Bandpass Filter Using 32nm CNTFET-Based MOCCCII
Mirnezamis, Shabnam
Dousti, Massoud
Dolatshahi, Mehdi
JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS, 2024, 33 (10)
[22] ADP-insensitive phosphoenzyme intermediate of sarcoplasmic reticulum Ca2+-ATPase has a compact conformation resistant to proteinase K, V8 protease and trypsin
Danko, S
Daiho, T
Yamasaki, K
Kamidochi, M
Suzuki, H
Toyoshima, C
FEBS LETTERS, 2001, 489 (2-3): : 277 - 282
[23] Compact operators and integral equations in the ℋK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal H}{\cal K}$$\end{document} space
Varayu Boonpogkrong
Czechoslovak Mathematical Journal, 2022, 72 (1) : 239 - 257
[24] If K is a Valdivia compact space, then Cp(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{\hspace{-1.111pt}p}(K)$$\end{document} is uniformly ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-separable
Joel Aguilar-Velázquez
Reynaldo Rojas-Hernández
Vladimir V. Tkachuk
European Journal of Mathematics, 2023, 9 (4)

← 1 2 3 →