Uniformizable Functional Alexandroff Spaces

Ayatollah Zadeh Shirazi, Fatemah; Hakimi, Elaheh; Hosseini, Arezoo; Rezavand, Reza

doi:10.22091/maa.2025.14446.1037

Uniformizable Functional Alexandroff Spaces

Document Type : Original Article

Authors

Fatemah Ayatollah Zadeh Shirazi ¹
Elaheh Hakimi ¹
Arezoo Hosseini ²
Reza Rezavand ¹

¹ Faculty of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran.

² Department of Mathematics Education, Farhangian University, Tehran, Iran.

10.22091/maa.2025.14446.1037

Abstract

In the following text, we show that the Alexandroff space X is uniformizable if and only if the collection of all smallest neighbourhoods is a partition of X. Moreover the Alexandroff space X is uniformizable and functional Alexandroff (k−primal) if and only if the collection of all smallest neighbourhoods is a partition of X into its finite subsets.

Keywords