Proper maps for lax algebras and the Kuratowski-Mrówka Theorem

Abstract

The characterization of stably closed maps of topological spaces as the closed maps with compact fibres and the role of the Kuratowski-Mrowka' Theorem in this characterization are being explored in the general context of lax (T; V )-algebras, for a quantale V and a Set-monad T with a lax extension to V -relations. The general results are being applied in standard (topological and metric) and non-standard (labeled graphs) contexts.