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Mazur spaces.

Wilansky, Albert (1981)

International Journal of Mathematics and Mathematical Sciences

Mazur-like topological linear spaces and their products

Miroslav Hušek (1997)

Commentationes Mathematicae Universitatis Carolinae

Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.

Mesocompactness and selection theory

Peng-fei Yan, Zhongqiang Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

A topological space X is called mesocompact (sequentially mesocompact) if for every open cover 𝒰 of X , there exists an open refinement 𝒱 of 𝒰 such that { V 𝒱 : V K } is finite for every compact set (converging sequence including its limit point) K in X . In this paper, we give some characterizations of mesocompact (sequentially mesocompact) spaces using selection theory.

Metrizable completely distributive lattices

Zhang De-Xue (1997)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space X , let C F ( X ) be the family of hypographs of all continuous maps from X to [ 0 , 1 ] endowed with the Fell topology. It is proved that X has a dense separable metrizable locally compact open subset if C F ( X ) is metrizable. Moreover, for a first-countable space X , C F ( X ) is metrizable if and only if X itself is a locally compact separable metrizable space. There exists a Tychonoff space X such that C F ( X ) is metrizable but X is not first-countable.

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