Quasi-Uniformities and Quotients of Paratopological Groups

Abstract

For a subgroup H of a paratopological group G we prove that the quotient topology of the coset space G / H is induced by a rotund quasi-uniformity and the quotient topology of the semiregularization ( G / H ) sr of G / H is induced by a normal quasi-uniformity. In particular, ( G / H ) sr is a Tychono ff space provided that G / H is Hausdor ff . The previous results are applied in order to show that every Hausdor ff Lindel ̈ of paratopological group is ω -admissible. We also show that, if G is an ω -admissible paratopological group, then so are the reflections T i ( G ) (i = 0,1,2,3), Re 1 ( G ) and Tych ( G )