3 papers
math.LO2026
The Cofinality of Generating Familes
Paul Gartside, Thomas Gilton
The topology of a separable metrizable space is \emph{generated} by a family of its subsets provided that a set is closed in if and only if $A\…
math.LO2025
Forcing Axioms for Proper Posets Preserving a Topological Property: Consistency Results
Thomas Gilton
Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we…
math.LO2024
Preservation of Topological Properties by Strongly Proper Forcings
Thomas Gilton, Jared Holshouser
In this paper we show that forcings which are strongly proper for stationarily many countable elementary submodels preserve each of the following properties of topological spaces:…