On a stronger form of hereditary compactness in product spaces

More on sg-compact spaces

The aim of this paper is to continue the study of sg-compact spaces, a topological notion much stronger than hereditary compactness. We investigate the relations between sg-compact and $C_2$-spaces and the interrelations to hereditarily sg-closed sets.

SI-紧空间的两个问题

Two problems of SI-compact spaces

本文针对SI-紧空间的两个问题，证明有限个SI-紧空间的乘积仍为SI-紧空间，正面回应了前人的问题，并得出SI-紧空间范畴不是TOP的反射满子范畴的结论。

一种构造紧且非SI紧空间的新方法

A new method for constructing a compact and non SI-compact space

本文提出构造紧且非SI紧空间的新方法，引入v紧性概念并证明其相关性质，解答了Zhao、Ho及[1]提出的问题。

Between countably compact and $ω$-bounded

Given a property $P$ of subspaces of a $T_1$ space $X$, we say that $X$ is {\em $P$-bounded} iff every subspace of $X$ with property $P$ has compact closure in $X$. Here we study $P$-bounded spaces for the properties $P \in \{ωD, ωN, C_2 \}$ where $ωD \, \equiv$ "countable discrete", $ωN \, \equiv$ "countable nowhere dense", and $C_2 \,\equiv$ "second countable". Clearly, for each of these $P$-bounded is between countably compact and $ω$-bounded. We give examples in ZFC that separate all these boundedness properties and their appropriate combinations. Consistent separating examples with better…