Generating countable sets of continuous selfmaps on IN-absorbing spaces

Abstract

S(X) is the semigroup, under composition, of all continuous selfmaps of the topological space X. In this paper, Banach's method in [8] is adapted to show that every countable subset of S(X) is contained in a 2- generated subsemigroup of S(X) when X is an IN-absorbing  space.