A note on almost periodic points and minimal sets in \(T_{1}\)- and \(T_{2}\)-spaces (Q937007)
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scientific article; zbMATH DE number 5314254
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on almost periodic points and minimal sets in \(T_{1}\)- and \(T_{2}\)-spaces |
scientific article; zbMATH DE number 5314254 |
Statements
A note on almost periodic points and minimal sets in \(T_{1}\)- and \(T_{2}\)-spaces (English)
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20 August 2008
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Summary: We show that (1) there exist almost periodic orbits in \(T_{2}\)-spaces of which the closures are not minimal sets; (2) there exist minimal sets in locally compact \(T_{1}\)-spaces which are not compact; (3) there exist almost periodic orbits in \(T_{2}\)-spaces of which the closures contain not only almost periodic points. These give answers to the three problems given by \textit{J. H. Mai} and \textit{W. H. Sun} [Topology Appl. 154, No.~15, 2873--2879 (2007; Zbl 1202.54029)].
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