On g-pseudo-contractibility of continua

Abstract

Let f and g be maps between topological spaces X and Y. The maps f and g are called pseudo-homotopic provided that there exist a continuum C, points a, b ∈ C and a map H: X × C → Y such that H(x, a) = g(x) and H(x, b) = f(x). The map H is called a pseudo-homotopy between f and g. A topological space X is said to be g-pseudo-contractible provided that there exists a pseudo-homotopy between an onto map from X to X and a constant map. The main purpose of this paper is to present the concept of g-pseudo-contractibility that generalizes the notions of g-contractibility and pseudo-contractibility showing general facts about it.