Open uniform (G) at non-isolated points and maps

TL;DR

This paper introduces the concept of open uniform (G) at non-isolated points, characterizes spaces with this property as open boundary-compact images of metric spaces, and explores inverse images and open questions related to this notion.

Contribution

It defines a new topological property and characterizes it via images of metric spaces, expanding understanding of space mappings and properties.

Findings

Spaces with open uniform (G) at non-isolated points are exactly the open boundary-compact images of metric spaces.

The paper discusses the inverse images of such spaces.

Poses open questions about the property.

Abstract

In this paper, we mainly introduce the notion of an open uniform (G) at non-isolated points, and show that a space $X$ has an open uniform (G) at non-isolated points if and only if $X$ is the open boundary-compact image of metric spaces. Moreover, we also discuss the inverse image of spaces with an open uniform (G) at non-isolated points. Two questions about open uniform (G) at non-isolated points are posed.