Spaces in which compact subsets are closed and the lattice of $T_1$-topologies on a set

Ofelia Teresa Alas; Richard Gordon Wilson

Displaying similar documents to “Spaces in which compact subsets are closed and the lattice of $T_{1}$ -topologies on a set”

Further remarks on KC and related spaces

Angelo Bella, Camillo Costantini (2011)

Commentationes Mathematicae Universitatis Carolinae

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A topological space is KC when every compact set is closed and SC when every convergent sequence together with its limit is closed. We present a complete description of KC-closed, SC-closed and SC minimal spaces. We also discuss the behaviour of the finite derived set property in these classes.

On cardinal invariants

Archangelskij, A. V.

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On weakly monotonically monolithic spaces

Liang-Xue Peng (2010)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a $D$ -space. Thus most known conclusions on $D$ -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space $X$ is sequential and has a point-countable $w c s^{*}$ -network then $X$ is a $D$ -space.

Displaying similar documents to “Spaces in which compact subsets are closed and the lattice of T 1 -topologies on a set”

Further remarks on KC and related spaces

On cardinal invariants

On weakly monotonically monolithic spaces

Displaying similar documents to “Spaces in which compact subsets are closed and the lattice of $T_{1}$ -topologies on a set”