On linear homeomorphisms of spaces of continuous functions on Hattori spaces

摘要

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 C-p(H(A)), C-p(H(B)) and C-p(S), where H(A) and H(B) are Hattori spaces and S is Sorgenfrey line. (C) 2020 Elsevier B.V. All rights reserved.