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

TL;DR

This paper investigates the internal structure of certain homogeneous metric spaces and explores properties of specific non-separable absolute F_{σδ} and G_{δσ} sets, contributing to the understanding of their homogeneity and topological characteristics.

Contribution

It provides an internal description of the space Q(k)^ and analyzes the dense homogeneity of the Baire space B(k) for k > , along with properties of non-separable absolute F_{σδ} and G_{δσ} sets.

Findings

Q(k)^ has an explicit internal description.

Baire space B(k) is densely homogeneous for k > .

Properties of non-separable absolute F_{σδ} and G_{δσ} sets are characterized.

Abstract

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 the Baire 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.