TL;DR
This paper introduces a topological space that is regular but not completely regular, characterized by all closed sets being $G_eta$-sets and each singleton being a zero-set, highlighting subtle distinctions in regularity.
Contribution
It constructs and analyzes a space with specific regularity properties that challenge traditional classifications in topology.
Findings
All closed sets are $G_eta$-sets.
Every singleton is a zero-set.
The space is regular but not completely regular.
Abstract
The purpose of this note is to describe a space that is regular but not completely regular, but only barely so: all closed sets are -sets and every singleton is a zero-set.
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