A note on functional tightness and minitightness of space of the G -permutation degree

Dimitrios N. Georgiou; Nodirbek K. Mamadaliev; Rustam M. Zhuraev

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 1, page 97-108
  • ISSN: 0010-2628

Abstract

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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 τ -open sets and investigate some basic properties of them. b) We prove that if the map f : X → Y is τ -continuous, then the map S P n f : S P n X → S P n Y is also τ -continuous. c) We show that the functor S P n preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on τ -bounded spaces. More precisely, we prove that the functor of permutation degree S P n preserves the property of being τ -bounded.

How to cite

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Georgiou, Dimitrios N., Mamadaliev, Nodirbek K., and Zhuraev, Rustam M.. "A note on functional tightness and minitightness of space of the $G$-permutation degree." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 97-108. <http://eudml.org/doc/299532>.

@article{Georgiou2023,
abstract = {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 $-bounded.},
author = {Georgiou, Dimitrios N., Mamadaliev, Nodirbek K., Zhuraev, Rustam M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\tau $-open set; $\tau $-bounded space; functional tightness; minimal tightness},
language = {eng},
number = {1},
pages = {97-108},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on functional tightness and minitightness of space of the $G$-permutation degree},
url = {http://eudml.org/doc/299532},
volume = {64},
year = {2023},
}

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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 97
EP - 108
AB - 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.
LA - eng
KW - $\tau $-open set; $\tau $-bounded space; functional tightness; minimal tightness
UR - http://eudml.org/doc/299532
ER -

References

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