Topological extensions with compact remainder
M. R. Koushesh

TL;DR
This paper explores the relationship between the order structure of certain topological extensions of a space with compact remainder and the topology of subspaces of its Stone-Čech compactification, focusing on pseudocompactness and realcompactness.
Contribution
It establishes connections between the order structure of $rak{P}$-extensions and the topology of subspaces of $eta X ackslash X$, specifically for pseudocompactness and realcompactness.
Findings
Characterizes the order structure of $rak{P}$-extensions with compact remainder.
Analyzes the topology of subspaces of $eta X ackslash X$ related to these extensions.
Provides detailed results for pseudocompactness and realcompactness cases.
Abstract
Let be a topological property. We study the relation between the order structure of the set of all -extensions of a completely regular space with compact remainder (partially ordered by the standard partial order ) and the topology of certain subspaces of the outgrowth . The cases when is either pseudocompactness or realcompactness are studied in more detail.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topology and Set Theory · Advanced Topics in Algebra
