# $Ps$-normal and $Ps$-Tychonoff spaces

## TL;DR

This paper introduces $Ps$-normal and $Ps$-Tychonoff spaces, exploring their properties and relationships with other normality concepts in topology, and establishing connections with various classes of spaces.

## Contribution

It defines new classes of spaces based on bijections to normal or Tychonoff spaces that preserve homeomorphisms on pseudocompact subsets and analyzes their relations with existing normality concepts.

## Key findings

- Established relations between $Ps$-normal, $Ps$-Tychonoff, and other normal spaces.
- Connected $C$-normal, $CC$-normal, $L$-normal, $C$-Tychonoff, $CC$-Tychonoff spaces with $Ps$-normal concepts.
- Provided characterizations and properties of these new classes in the context of topological normality.

## Abstract

A space $X$ is called $Ps$-normal($Ps$-Tychonoff) space if there exists a normal(Tychonoff) space $Y$ and a bijection $f: X\mapsto Y$ such that $f\lvert_K:K\mapsto f(K)$ is homeomorphism for any pseudocompact subset $K$ of $X$. We establish a few relations between $C$-normal, $CC$-normal, $L$-normal, $C$-Tychonoff, $CC$-Tychonoff spaces with $Ps$-normal and $Ps$-Tychonoff spaces.