Uniform bases at non-isolated points and maps

TL;DR

This paper investigates how spaces with an uniform base at non-isolated points behave under various types of continuous maps, revealing preservation properties and limitations of decomposition theorems.

Contribution

It establishes that perfect, open, and closed maps preserve spaces with an uniform base at non-isolated points, and shows the failure of the decomposition theorem in this context.

Findings

Perfect maps preserve spaces with an uniform base at non-isolated points.

Open and closed maps preserve regular spaces with an uniform base at non-isolated points.

Spaces with an uniform base at non-isolated points do not satisfy the decomposition theorem.

Abstract

In this paper, the authors mainly discuss the images of spaces with an uniform base at non-isolated points, and obtain the following main results: (1)\ Perfect maps preserve spaces with an uniform base at non-isolated points; (2)\ Open and closed maps preserve regular spaces with an uniform base at non-isolated points; (3)\ Spaces with an uniform base at non-isolated points don't satisfy the decomposition theorem.