Minimal $KC$-spaces are countably compact

Theodoros Vidalis

Displaying similar documents to “Minimal $K C$ -spaces are countably compact”

On minimal strongly KC-spaces

Weihua Sun, Yuming Xu, Ning Li (2009)

Czechoslovak Mathematical Journal

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In this article we introduce the notion of strongly $KC$ -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space $(X, τ)$ is maximal countably compact if and only if it is minimal strongly $KC$ , and apply this result to study some properties of minimal strongly $KC$ -spaces, some of which are not possessed by minimal $KC$ -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether...

On Manes' countably compact, countably tight, non-compact spaces

James Dabbs (2011)

Commentationes Mathematicae Universitatis Carolinae

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We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.

Spaces in which compact subsets are closed and the lattice of $T_{1}$ -topologies on a set

Ofelia Teresa Alas, Richard Gordon Wilson (2002)

Commentationes Mathematicae Universitatis Carolinae

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We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of $T_{1}$ -topologies on a set $X$ .

A note on paratopological groups

Chuan Liu (2006)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, it is proved that a first-countable paratopological group has a regular $G_{δ}$ -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [, Topology Appl. (2006), 1917–1929]. If $G$ is a symmetrizable paratopological group, then $G$ is a developable space. We also discuss copies of $S_{ω}$ and of $S_{2}$ in paratopological groups and generalize some Nyikos [, Proc. Amer. Math. Soc. (1981), no. 4, 793–801] and Svetlichnyi [, Vestnik Moskov. Univ. Ser. I Mat. Mekh....

Displaying similar documents to “Minimal K C -spaces are countably compact”

On minimal strongly KC-spaces

On Manes' countably compact, countably tight, non-compact spaces

Spaces in which compact subsets are closed and the lattice of T 1 -topologies on a set

A note on paratopological groups

Displaying similar documents to “Minimal $K C$ -spaces are countably compact”

Spaces in which compact subsets are closed and the lattice of $T_{1}$ -topologies on a set