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 ( X 1 , k ) is homeomorphic to b ( X 2 , 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 Ind X = 0 and X = G ∪ L , where G is an absolute G δ and L is of first category, then X ω is an h-homogeneous space. We consider certain cases when A × X ω is homeomorphic to X ω providing A ⊂ X ω .