Tom Richmond, Josef Šlapal: Closure operators for semitopogenous spaces, 3-14

Abstract:

Semitopogenous orders on a set $X$ were introduced by Császár to provide a unified approach to topology, proximity, and uniformity. At least four closure operators associated with a semitopogenous order have been introduced by various authors. We provide a systematic comparison of these closure operators. Examples are presented to show their relative dependence and independence.

Key Words: Semitopogenous order, closure operator, topology, connected closure space.

2020 Mathematics Subject Classification: Primary 54A05; Secondary 54A15, 54A10.

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