$CCS$-normal spaces

TL;DR

This paper introduces the concept of $CCS$-normal spaces, exploring their properties and relationships with other types of normal spaces, by establishing conditions under which certain bijections preserve cellular-compact subsets.

Contribution

It defines $CCS$-normal spaces and investigates their connections with $C$-normal, $CC$-normal, and $Ps$-normal spaces, expanding the theory of space normality.

Findings

$CCS$-normal spaces are characterized by existence of a bijection to a normal space preserving cellular-compact subsets.

Relations between $CCS$-normal and other normal spaces are established.

Conditions under which $CCS$-normality implies or is implied by other normality properties are discussed.

Abstract

A space $X$ is called $CCS$-normal space if there exist a normal space $Y$ and a bijection $f: X\mapsto Y$ such that $f\lvert_C:C\mapsto f(C)$ is homeomorphism for any cellular-compact subset $C$ of $X$. We discuss about the relations between $C$-normal, $CC$-normal, $Ps$-normal spaces with $CCS$-normal.