On Normal Ideal Topological Spaces

Document Type : Original Article

Authors

Amin Talabeigi ¹

Ghasem Mirhosseini ²

Ali Shahrezaee ³

¹ Department of Mathematics‎, ‎Payame Noor University‎, ‎P.O‎. ‎Box‎, ‎19395-4697‎, ‎Tehran‎, ‎Iran.

² Department of Mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran.

³ Ph.D. student. Department of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-4697, Tehran, Iran.

10.22034/kjm.2025.506449.3459

Abstract

An ideal on a set $X$ is defined as a non-empty collection of subsets of $X$ that is closed under taking subsets (i.e., hereditary) and finite unions. Extensions of classical separation axioms on topological spaces can be defined using ideals. A notable and interesting extension of the normality axiom, termed $\mathcal{P}$-normality, was recently introduced by Pach'on Rubiano. In this paper, we investigate the properties of this separation axiom and provide several characterizations. In particular, we establish generalizations of both Urysohn's lemma and the Tietze extension theorem within this framework.

Keywords

Ideal

ideal space

normal

P-normal

P-completely regular

Subjects

• 54 General topology

---