Homeomorphisms between function spaces

Abstract

Given a space \(X\) and topological group \(H\), \(C(X,H)\) denotes the set of all continuous functions from a space \(X\) to a topological group \(H\). For a subset \(A\) of a space \(X\), \(X/A\) denotes the quotient space with quotient topology obtained from \(X\) by identifying \(A\) to a point. We study some homeomorphisms between \(C(X,H)\) and \(C(Y,H)\) for different \(X\) and \(Y\) under the point-open topology, open-point topology and bi-point-open topology.