Geodesic
A note on functional tightness and minitightness of space of the $G$-permutation degree
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 97-108.

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

We study the behavior of the minimal tightness and functional tightness of topological spaces under the influence of the functor of the permutation degree. Analytically: a) We introduce the notion of $\tau$-open sets and investigate some basic properties of them. b) We prove that if the map $f\colon X\rightarrow Y$ is $\tau$-continuous, then the map $SP^{n}f\colon SP^n X \rightarrow SP^n Y$ is also $\tau$-continuous. c) We show that the functor $SP^n$ preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on $\tau$-bounded spaces. More precisely, we prove that the functor of permutation degree $SP^n$ preserves the property of being $\tau$-bounded.
DOI : 10.14712/1213-7243.2023.019
Classification : 54B20, 54C05
Keywords: $\tau$-open set; $\tau$-bounded space; functional tightness; minimal tightness 
@article{10_14712_1213_7243_2023_019,
     author = {Georgiou, Dimitrios N. and Mamadaliev, Nodirbek K. and Zhuraev, Rustam M.},
     title = {A note on functional tightness and minitightness of space of the $G$-permutation degree},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {97--108},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {2023},
     doi = {10.14712/1213-7243.2023.019},
     mrnumber = {4631793},
     zbl = {07790585},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.019/}
}
TY  - JOUR
AU  - Georgiou, Dimitrios N.
AU  - Mamadaliev, Nodirbek K.
AU  - Zhuraev, Rustam M.
TI  - A note on functional tightness and minitightness of space of the $G$-permutation degree
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2023
SP  - 97
EP  - 108
VL  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.019/
DO  - 10.14712/1213-7243.2023.019
LA  - en
ID  - 10_14712_1213_7243_2023_019
ER  - 
%0 Journal Article
%A Georgiou, Dimitrios N.
%A Mamadaliev, Nodirbek K.
%A Zhuraev, Rustam M.
%T A note on functional tightness and minitightness of space of the $G$-permutation degree
%J Commentationes Mathematicae Universitatis Carolinae
%D 2023
%P 97-108
%V 64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.019/
%R 10.14712/1213-7243.2023.019
%G en
%F 10_14712_1213_7243_2023_019
Georgiou, Dimitrios N.; Mamadaliev, Nodirbek K.; Zhuraev, Rustam M. A note on functional tightness and minitightness of space of the $G$-permutation degree. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 97-108. doi : 10.14712/1213-7243.2023.019. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.019/

Cité par Sources :