Some relative properties on normality and paracompactness, and their absolute embeddings

Shinji Kawaguchi; Ryoken Sokei

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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 $X_{A} \times Y$ in connection with the normality of ${(X \times Y)}_{(A \times Y)}$ . The cases for paracompactness,...