Metrizable DH-spaces with a dense complete subset

TL;DR

This paper characterizes h-homogeneous spaces with dense complete subsets by proving their equivalence to being sigma-discretely controlled, providing a new understanding of their structure.

Contribution

It establishes the equivalence between dense homogeneity with a dense complete subspace and sigma-discrete control in h-homogeneous spaces, a novel characterization.

Findings

H-homogeneous spaces with dense complete subsets are sigma-discretely controlled.

The equivalence provides a new criterion for identifying such spaces.

This advances the understanding of the structure of metrizable DH-spaces.

Abstract

It is proved that for an h-homogeneous space X the following conditions are equivalent: 1) X is a densely homogeneous space with a dense complete subspace; 2) X is $\sigma$-discretely controlled.