On properties of h-homogeneous spaces with the Baire property

Abstract

We describe how to assign an h-homogeneous space b(X, k) with a dense complete subspace and of weight k to any strongly zero-dimensional metric space X of weight ≤k. We investigate the properties of such spaces and obtain the conditions when b(X1, k) is homeomorphic to b(X2, k). The h-homogeneous separable space T which is a union of B(ω) and a countable subspace was constructed by E. van Douwen. Similarly, the h-homogeneous separable space S which is a union of B(ω) and a σ-compact subspace was described by J. van Mill. These spaces are generalized for the non-separable case. We prove that if IndX=0 and X=G∪L, where G is an absolute Gδ and L is of first category, then Xω is an h-homogeneous space. We consider certain cases when A×Xω is homeomorphic to Xω providing A⊂Xω. © 2011 Elsevier B.V.