Cardinal Invariants for the $G_\delta$ topology

TL;DR

This paper establishes upper bounds on key topological invariants for the $G_\delta$-topology and applies these bounds to prove a recent result on the cardinality of certain homogeneous compact spaces.

Contribution

It provides new upper bounds for spread, Lindel"of number, and weak Lindel"of number in the $G_\delta$-topology, and offers a concise proof of a recent cardinality result.

Findings

Upper bounds for spread, Lindel"of, and weak Lindel"of numbers established.

Short proof of Juhász and van Mill's result on $\sigma$-countably tight homogeneous compacta.

Enhanced understanding of $G_\delta$-topology properties.

Abstract

We prove upper bounds for the spread, the Lindel\"of number and the weak Lindel\"of number of the $G_\delta$-topology on a topological space and apply a few of our bounds to give a short proof to a recent result of Juh\'asz and van Mill regarding the cardinality of a $\sigma$-countably tight homogeneous compactum.