On properties of h-homogeneous spaces of first category

A metric space X is called h-homogeneous if Ind X = 0 and each nonempty open-closed subset of X is homeomorphic to X. We describe how to assign an h-homogeneous space of first category and of weight k to any strongly zero-dimensional metric space of weight ⩽k. We investigate the properties of such spaces. We show that if Q is the space of rational numbers and Y is a strongly zero-dimensional metric space, then Q × Y ω is an h-homogeneous space and F × Q × Y ω is homeomorphic to Q × Y ω for any F σ -subset F of Q × Y ω . L. Keldysh proved that any two canonical elements of the Borel class α are homeomorphic. The last theorem is generalized for the nonseparable case.