Merotopies associated with quasi-uniformities

Abstract

To an arbitrary quasi-uniformity on the set X, a merotopy on X is assigned. There are results concerning the question whether this merotopy is compatible with the topology induced by the quasi-uniformity end whether the closure operation induced by the merotopy, admits a compatible uniformity. More precise results are obtained in the case of transitive quasi-uniformities.

Keywords

• Quasi-uniformity
• Merotopy
• Semi-symmetric
• Transitive