A pseudocompactification

TL;DR

This paper introduces a new maximal pseudocompactification for locally pseudocompact spaces, expanding understanding of their structure and properties.

Contribution

It defines and characterizes the largest pseudocompactification with compact remainder for locally pseudocompact spaces, providing new insights into their topological structure.

Findings

Z X is the largest pseudocompactification with compact remainder.

Characterizations of Z X are provided.

The paper establishes the partial order relation among pseudocompactifications.

Abstract

For a locally pseudocompact space $X$ let [\zeta X=X\cup cl_{\beta X}(\beta X\backslash\upsilon X).] It is proved that $\zeta X$ is the largest (with respect to the standard partial order $\leq$) among all pseudocompactifications of $X$ which have compact remainder. Other characterizations of $\zeta X$ are also given.