A class of nontrivial simple examples of a non-D-space

Pub Date : 2024-06-25 DOI:10.1515/gmj-2024-2033

Yu-Lin Chou

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引用次数: 0

Abstract

Given any regular T 0

{T_{0}}

(equivalently, regular T 1

{T_{1}}

) space X, the question of whether X being Lindelöf implies X being a D-space is an active open problem. This article gives a class of handy examples of a second countable collectionwise normal collectionwise Hausdorff T 0

{T_{0}}

space of uncountable cardinal, with at most countably many singletons being not closed, that is not a D-space. Also given is a class of handy examples of a second countable hyperconnected T 0

{T_{0}}

space of uncountable cardinal, with at most countably many singletons being not closed, that is not a D-space.

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一类非微不足道的非 D 空间简单示例

给定任何正则 T 0 {T_{0}} （等价于正则 T 1 {T_{1}} ）空间 X (等价地，正则 T 1 {T_{1}} ）空间 X，X 是林德洛夫是否意味着 X 是 D 空间是一个活跃的开放问题。本文给出了一类非 D 空间的第二可数集合正则集合 Hausdorff T 0 {T_{0}}空间的方便例子，该空间具有最多可数的单子不封闭。此外，还给出了一类非 D 空间的第二可数超连接 T 0 {T_{0}} 空间的方便示例，该空间具有最多可数个不封闭的单子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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