Metrizable DH-spaces of the first category

2014/01/30 by Medvedev, Sergey
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1401.7964

Abstract

We show that if a separable space X has a meager open subset containing a copy of the Cantor set 2^ω, then X has \frakc types of countable dense subsets. We suggest a generalization of the λ-set for non-separable spaces. Let X be an h-homogeneous Λ-set. Then X is densely homogeneous and (X ∖ A) is homeomorphic to X for every σ-discrete A ⊂ X.

Related

• Metrizable DH-spaces with a dense complete subset
• Zero-dimensional metrizable CDH space X such that X² is not CDH
• σ-homogeneity of Borel sets
• Non-separable h-homogeneous absolute F_σδ-spaces and G_δσ-spaces
• Countable dense homogeneity and topological groups