Consonant spaces of countable type and the Menger property

We investigate the connection between consonance and the Menger property. It has been shown that consonant metric spaces are Menger at infinity. We improve this result by showing that completely regular consonant spaces of countable type are Menger at infinity. This result will follow from a number of results about topological games in spaces that are more general than completely regular spaces.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This research investigates the connection between consonance and the Menger property. Previous studies have shown that consonant metric spaces exhibit the Menger property at infinity. We enhance this finding by demonstrating that completely regular consonant spaces of countable type also possess the Menger property at infinity, which is supported by results from topological games in spaces that are more general than completely regular spaces.