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Denote by Q(k) a \sigma-discrete metric weight-homogeneous space of weight k.We give an internal description of the space Q(k)^\omega. We prove that theBaire space B(k) is densely homogeneous with respect to Q(k)^\omega if k >\omega. Properties of some non-separable h-homogeneous absolute F_{\sigma\delta}-sets and G_{\delta \sigma}-sets are investigated.

Non-separable h-homogeneous absolute F_{\sigma \delta}-spaces and G_{\delta \sigma}-spaces