Relative normality and product spaces

Hoshina, Takao, and Sokei, Ryoken. "Relative normality and product spaces." Commentationes Mathematicae Universitatis Carolinae 44.3 (2003): 515-524. <http://eudml.org/doc/249185>.

@article{Hoshina2003,
abstract = {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 $X \setminus A$ 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, more generally, for $\gamma $-paracompactness will also be discussed for $X_A\times Y$. As an application, we prove that for a metric space $X$ with $A \subset X$ and a countably paracompact normal space $Y$, $X_A \times Y$ is normal if and only if $X_A \times Y$ is countably paracompact.},
author = {Hoshina, Takao, Sokei, Ryoken},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {strongly normal in; normal; $\gamma $-paracompact; product spaces; weak $C$-embedding; strongly normal in; normal; -paracompact; product; weak -embedding},
language = {eng},
number = {3},
pages = {515-524},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relative normality and product spaces},
url = {http://eudml.org/doc/249185},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Hoshina, Takao
AU - Sokei, Ryoken
TI - Relative normality and product spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 3
SP - 515
EP - 524
AB - 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 $X \setminus A$ 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, more generally, for $\gamma $-paracompactness will also be discussed for $X_A\times Y$. As an application, we prove that for a metric space $X$ with $A \subset X$ and a countably paracompact normal space $Y$, $X_A \times Y$ is normal if and only if $X_A \times Y$ is countably paracompact.
LA - eng
KW - strongly normal in; normal; $\gamma $-paracompact; product spaces; weak $C$-embedding; strongly normal in; normal; -paracompact; product; weak -embedding
UR - http://eudml.org/doc/249185
ER -