On properties of h-homogeneous spaces with the Baire property

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 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.