Uniformizable functional Alexandroff spaces

نویسندگان
Hosseini, Arezoo ID 1
Rezavand, Reza ID 2
Ayatollah Zadeh Shirazi, Fatemah ID 3
Hakimi, Elaheh ID 4

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

2 School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran.

3 School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran.

4 School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran.

doi
10.22091/maa.2025.14446.1037
چکیده

In this paper, 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.

کلیدواژه‌ها
Alexandroff space, Functional Alexandroff space, (k−)Primal space, topological group, Uniformizable