On the semigroups of quasi-open transformations

Abstract

In this paper we consider the semigroups of quasi-open transformations. A map f between topological spaces X and Y is quasi-open if for any non-empty open set U ⊂ X, the interior of f (U) in Y is non-empty. We give abstract characterizations of semigroups of continuous quasi-open transformations defined on an open set of Euclidean n-space and semigroups of quasi-open mappings defined on a certain class of topological spaces.