H-covering Maps in Descriptive Function Theory

2026/07/23 by Alexey Ostrovsky · 1 voice
#math.GN

paper · pdf

Abstract

We study the preservation of complete metrizability under maps between metric spaces. Two main approaches have been developed in this area: one based on the behavior of maps on countable compact sets, and another based on abstract conditions such as stability. In earlier work the author introduced the class of H-covering maps and proved that every such map is stable. The main result of this paper is the converse: a map is H-covering if and only if it is stable. This provides a concrete and practical description of stable maps and offers a unified framework for completeness-preserving mappings.

Discussions

• Alexey Ostrovsky: H-covering Maps in Descriptive Function Theory https://arxiv.org/abs/2607.21149 https://arxiv.org/pdf/2607.21149 https://arxiv.org/html/2607.21149 [bsky, 0 points, 0 comments]

Related

• Some New Questions on Point-countable Covers and Sequence-covering Mappings
• Exactly k-to-1 maps: from pathological functions with finitely many discontinuities to well-behaved covering maps
• On the expansiveness of coarse maps between Banach spaces and geometry preservation
• Stability Theorems in Pointwise Dynamics
• Sets of invariant measures and Cesaro stability