Uniformizable functional Alexandroff spaces

Document Type : Original Article

Authors

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

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

Abstract

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.

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References

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