Quasi-open functions in Euclidean spaces

Abstract

In this paper we consider the semigroups of quasi-open functions. A function 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 characterization of semigroups  of quasi-open functions defined on an open set of Euclidean n-space.