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

Kaori Yamazaki

Displaying similar documents to “Aull-paracompactness and strong star-normality of subspaces in topological spaces”

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,...

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

Shinji Kawaguchi, Ryoken Sokei (2005)

Commentationes Mathematicae Universitatis Carolinae

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Paracompactness ( $= 2$ -paracompactness) and normality of a subspace $Y$ in a space $X$ defined by Arhangel’skii and Genedi [4] are fundamental in the study of relative topological properties ([2], [3]). These notions have been investigated by primary using of the notion of weak $C$ - or weak $P$ -embeddings, which are extension properties of functions defined in [2] or [18]. In fact, Bella and Yaschenko [8] characterized Tychonoff spaces which are normal in every larger Tychonoff space, and this result...

Strongly base-paracompact spaces

John E. Porter (2003)

Commentationes Mathematicae Universitatis Carolinae

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A space $X$ is said to be if there is a basis $ℬ$ for $X$ with $| ℬ | = w (X)$ such that every open cover of $X$ has a star-finite open refinement by members of $ℬ$ . Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions $ℱ$ with cardinality equal to the weight such that every open cover has a locally finite partition of unity subordinated to it from $ℱ$ .