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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.

Metric-fine uniform frames

Joanne L. Walters-Wayland (1998)

Commentationes Mathematicae Universitatis Carolinae

A locallic version of Hager’s metric-fine spaces is presented. A general definition of 𝒜 -fineness is given and various special cases are considered, notably 𝒜 = all metric frames, 𝒜 = complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.

Monotone meta-Lindelöf spaces

Yin-Zhu Gao, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf G O -spaces in their linearly ordered extensions are revealed.

Monotone weak Lindelöfness

Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera (2011)

Open Mathematics

The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces...

More about spaces with a small diagonal

Alan Dow, Oleg Pavlov (2006)

Fundamenta Mathematicae

Hušek defines a space X to have a small diagonal if each uncountable subset of X² disjoint from the diagonal has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a compact space of weight ω₁ which has a small diagonal will be metrizable, but it remains an open problem to determine if the weight restriction is necessary. It has been shown to be consistent that each compact space with a small diagonal is metrizable; in particular, Juhász and Szentmiklóssy proved...

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