Some New Questions on Point-countable Covers and Sequence-covering Mappings

TL;DR

This survey discusses 37 open questions related to point-countable covers and sequence-covering mappings within generalized metric spaces, highlighting some answered questions and exploring their implications.

Contribution

It compiles and analyzes key open problems in the theory of generalized metric spaces involving covers and mappings, providing insights and partial answers.

Findings

Some questions have been answered.

The questions relate to properties of generalized metric spaces.

The survey highlights open problems and partial solutions.

Abstract

In this survey, 37 questions on point-countable covers and sequence-covering mappings are listed, in which some of these questions have been answered. These questions are mainly related to the theory of generalized metric spaces, involving point-countable covers, sequence-covering mappings, images of metric spaces and hereditarily closure-preserving families.