Proximities and two types uniformities

Abstract

In a strictly two-sided, commutative biquantale, we introduce the notion of (<TEX>$L,\;{\odot}$</TEX>)-proximity spaces. We investigate the relations among (<TEX>$L,\;{\odot}$</TEX>)-proximity spaces, Hutton (<TEX>$L,\;{\otimes}$</TEX>)-uniform spaces, (<TEX>$L,\;{\odot}$</TEX>) uniform spaces, enriched (<TEX>$L,\;{\odot}$</TEX>)-topological spaces and enriched (<TEX>$L,\;{\odot}$</TEX>)-interior spaces.