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Let $P$ be a topological property. A space $X$ is said to be star P if whenever $𝒰$ is an open cover of $X$ , there exists a subspace $A \subseteq X$ with property $P$ such that $X = S t (A, 𝒰)$ . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.

A note on star compact spaces with a $G_{δ}$ -diagonal

Yan-Kui Song (2011)

Matematički Vesnik

A note on star Lindelöf, first countable and normal spaces

Wei-Feng Xuan (2017)

Mathematica Bohemica

A topological space $X$ is said to be star Lindelöf if for any open cover $𝒰$ of $X$ there is a Lindelöf subspace $A \subset X$ such that $St (A, 𝒰) = X$ . The “extent” $e (X)$ of $X$ is the supremum of the cardinalities of closed discrete subsets of $X$ . We prove that under $V = L$ every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under $MA + \neg CH$ , which shows that a star Lindelöf, first countable and normal space may not have countable extent.

A note on strong compactness and S-closedness

Atia R. H., S. N. El-Deeb, I. A. Hasanein (1982)

Matematički Vesnik

A note on the Bohr compactification.

M. Friedberg, J.W. Stepp (1974)

Semigroup forum

A note on the dimension Dind

W. Kulpa (1972)

Colloquium Mathematicae

A note on the extent of two subclasses of star countable spaces

Zuoming Yu (2012)

Open Mathematics

We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.

A note on the least element map

A. R. Bednarek (1969)

Colloquium Mathematicae

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

In this note we first give a summary that on property of a remainder of a non-locally compact topological group $G$ in a compactification $b G$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $b G$ such that the remainder $b G ∖ G$ of $G$ belongs to $𝒫$ , then $G$ and $b G ∖ G$ are separable and metrizable, where $𝒫$ is a class of spaces which satisfies the following conditions: (1) if $X \in 𝒫$ , then every compact subset of the space $X$ is a...

A note on topological properties of non-Hausdorff manifolds.

Kent, Steven L., Mimna, Roy A., Tartir, Jamal K. (2009)

International Journal of Mathematics and Mathematical Sciences

A note on transfinite sequences

Norman Howes (1980)

Fundamenta Mathematicae

A note on transitively $D$ -spaces

Liang-Xue Peng (2011)

Czechoslovak Mathematical Journal

In this note, we show that if for any transitive neighborhood assignment $φ$ for $X$ there is a point-countable refinement $ℱ$ such that for any non-closed subset $A$ of $X$ there is some $V \in ℱ$ such that $| V \cap A | \geq ω$ , then $X$ is transitively $D$ . As a corollary, if $X$ is a sequential space and has a point-countable $w c s^{*}$ -network then $X$ is transitively $D$ , and hence if $X$ is a Hausdorff $k$ -space and has a point-countable $k$ -network, then $X$ is transitively $D$ . We prove that if $X$ is a countably compact sequential space and has a point-countable...

Currently displaying 141 – 160 of 1977

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Displaying 141 – 160 of 1977

A note on semihomeomorphism between semi $T_{D}$ spaces

A note on separability of the Fell-hyperspace topology

A note on separation of sets by approximately continuous functions

A note on sequence-covering $π$ -images of metric spaces

A note on spaces with countable extent