On linear homeomorphisms of spaces of continuous functions on Hattori spaces

Abstract

For a subset A of the real line R, the Hattori space H(A) is a topological space whose underlying point set is the real R and whose topology is defined as follows: points from A possess the usual Euclidean neighbourhoods while remaining points are given the neighbourhoods of the Sorgenfrey line. We consider the linear homeomorphisms between the spaces Cp(H(A)), Cp(H(B)) and Cp(S), where H(A) and H(B) are Hattori spaces and S is Sorgenfrey line.