Geodesic
Factorizations of normality via generalizations of $\beta $-normality
Mathematica Bohemica, Tome 141 (2016) no. 4, pp. 463-473

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2016.0048-15
Classification : 54D15
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 
@article{10_21136_MB_2016_0048_15,
     author = {Das, Ananga Kumar and Bhat, Pratibha and Gupta, Ria},
     title = {Factorizations of normality via generalizations of $\beta $-normality},
     journal = {Mathematica Bohemica},
     pages = {463--473},
     publisher = {mathdoc},
     volume = {141},
     number = {4},
     year = {2016},
     doi = {10.21136/MB.2016.0048-15},
     mrnumber = {3576793},
     zbl = {06674856},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.0048-15/}
}
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
SP  - 463
EP  - 473
VL  - 141
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.0048-15/
DO  - 10.21136/MB.2016.0048-15
LA  - en
ID  - 10_21136_MB_2016_0048_15
ER  - 
%0 Journal Article
%A Das, Ananga Kumar
%A Bhat, Pratibha
%A Gupta, Ria
%T Factorizations of normality via generalizations of $\beta $-normality
%J Mathematica Bohemica
%D 2016
%P 463-473
%V 141
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.0048-15/
%R 10.21136/MB.2016.0048-15
%G en
%F 10_21136_MB_2016_0048_15
Das, Ananga Kumar; Bhat, Pratibha; Gupta, Ria. Factorizations of normality via generalizations of $\beta $-normality. Mathematica Bohemica, Tome 141 (2016) no. 4, pp. 463-473. doi: 10.21136/MB.2016.0048-15

Cité par Sources :