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On some classes of spaces with the D -property

Juan Carlos Martínez (2014)

Commentationes Mathematicae Universitatis Carolinae

We shall prove that under CH every regular meta-Lindelöf P -space which is locally D has the D -property. In addition, we shall prove that a regular submeta-Lindelöf P -space is D if it is locally D and has locally extent at most ω 1 . Moreover, these results can be extended from the class of locally D -spaces to the wider class of 𝔻 -scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology...

On star covering properties related to countable compactness and pseudocompactness

Marcelo D. Passos, Heides L. Santana, Samuel G. da Silva (2017)

Commentationes Mathematicae Universitatis Carolinae

We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that Ψ -spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if X is a star-compact space within a certain class, then X is neither first countable nor separable....

On 𝒞 -starcompact spaces

Yan-Kui Song (2008)

Mathematica Bohemica

A space X is 𝒞 -starcompact if for every open cover 𝒰 of X , there exists a countably compact subset C of X such that St ( C , 𝒰 ) = X . In this paper we investigate the relations between 𝒞 -starcompact spaces and other related spaces, and also study topological properties of 𝒞 -starcompact spaces.

On ℒ -starcompact spaces

Yan-Kui Song (2006)

Czechoslovak Mathematical Journal

A space X is ℒ -starcompact if for every open cover 𝒰 of X , there exists a Lindelöf subset L of X such that S t ( L , 𝒰 ) = X . We clarify the relations between ℒ -starcompact spaces and other related spaces and investigate topological properties of ℒ -starcompact spaces. A question of Hiremath is answered.

On the cardinality of Urysohn spaces and weakly H -closed spaces

Fortunata Aurora Basile, Nathan Carlson (2019)

Mathematica Bohemica

We introduce the cardinal invariant θ - a L ' ( X ) , related to θ - a L ( X ) , and show that if X is Urysohn, then | X | ≤ 2 θ - a L ' ( X ) χ ( X ) . As θ - a L ' ( X ) ≤ a L ( X ) , this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly H -closed spaces, related to H -closed spaces.

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