# Factorizations of normality via generalizations of $\beta $-normality

Ananga Kumar Das; Pratibha Bhat; Ria Gupta

Mathematica Bohemica (2016)

- Volume: 141, Issue: 4, page 463-473
- ISSN: 0862-7959

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topDas, Ananga Kumar, Bhat, Pratibha, and Gupta, Ria. "Factorizations of normality via generalizations of $\beta $-normality." Mathematica Bohemica 141.4 (2016): 463-473. <http://eudml.org/doc/287540>.

@article{Das2016,

abstract = {The notion of $\beta $-normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost $\beta $-normal spaces, which is a simultaneous generalization of $\beta $-normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak $\beta $-normality, in terms of $\theta $-closed sets, which turns out to be a simultaneous generalization of $\beta $-normality and $\theta $-normality. A space $X$ is said to be weakly $\beta $-normal (w$\beta $-normal$)$ if for every pair of disjoint closed sets $A$ and $B$ out of which, one is $\theta $-closed, there exist open sets $U$ and $V$ such that $\overline\{A\cap U\}=A$, $\overline\{B\cap V\}=B$ and $\overline\{U\}\cap \overline\{V\}=\emptyset $. It is shown that w$\beta $-normality acts as a tool to provide factorizations of normality.},

author = {Das, Ananga Kumar, Bhat, Pratibha, Gupta, Ria},

journal = {Mathematica Bohemica},

keywords = {normal space; (weakly) densely normal space; (weakly) $\theta $-normal space; almost normal space; almost $\beta $-normal space; $\kappa $-normal space; (weakly) $\beta $-normal space},

language = {eng},

number = {4},

pages = {463-473},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Factorizations of normality via generalizations of $\beta $-normality},

url = {http://eudml.org/doc/287540},

volume = {141},

year = {2016},

}

TY - JOUR

AU - Das, Ananga Kumar

AU - Bhat, Pratibha

AU - Gupta, Ria

TI - Factorizations of normality via generalizations of $\beta $-normality

JO - Mathematica Bohemica

PY - 2016

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 141

IS - 4

SP - 463

EP - 473

AB - The notion of $\beta $-normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost $\beta $-normal spaces, which is a simultaneous generalization of $\beta $-normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak $\beta $-normality, in terms of $\theta $-closed sets, which turns out to be a simultaneous generalization of $\beta $-normality and $\theta $-normality. A space $X$ is said to be weakly $\beta $-normal (w$\beta $-normal$)$ if for every pair of disjoint closed sets $A$ and $B$ out of which, one is $\theta $-closed, there exist open sets $U$ and $V$ such that $\overline{A\cap U}=A$, $\overline{B\cap V}=B$ and $\overline{U}\cap \overline{V}=\emptyset $. It is shown that w$\beta $-normality acts as a tool to provide factorizations of normality.

LA - eng

KW - normal space; (weakly) densely normal space; (weakly) $\theta $-normal space; almost normal space; almost $\beta $-normal space; $\kappa $-normal space; (weakly) $\beta $-normal space

UR - http://eudml.org/doc/287540

ER -

## References

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