Displaying similar documents to “Some relative properties on normality and paracompactness, and their absolute embeddings”

Aull-paracompactness and strong star-normality of subspaces in topological spaces

Kaori Yamazaki (2004)

Commentationes Mathematicae Universitatis Carolinae

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We prove for a subspace Y of a T 1 -space X , Y is (strictly) Aull-paracompact in X and Y is Hausdorff in X if and only if Y is strongly star-normal in X . This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].

Relative normality and product spaces

Takao Hoshina, Ryoken Sokei (2003)

Commentationes Mathematicae Universitatis Carolinae

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Arhangel’skiĭ defines in [Topology Appl. 70 (1996), 87–99], as one of various notions on relative topological properties, strong normality of A in X for a subspace A of a topological space X , and shows that this is equivalent to normality of X A , where X A denotes the space obtained from X by making each point of X ∖ A isolated. In this paper we investigate for a space X , its subspace A and a space Y the normality of the product X A × Y in connection with the normality of ( X × Y ) ( A × Y ) . The cases for paracompactness,...

On ℒ -starcompact spaces

Yan-Kui Song (2006)

Czechoslovak Mathematical Journal

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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.