P. Gartside

activity

20082026

most citedSpaces with a Finite Family of Basic Functions

8 citations · 17 across the 19 of their papers we have counts for

collaborators

26 papers

math.LO2026

The Cofinality of Generating Familes

Paul Gartside, Thomas Gilton

The topology of a separable metrizable space $M$ is \emph{generated} by a family $C$ of its subsets provided that a set $A \subseteq M$ is closed in $M$ if and only if $A\…

math.GN2025

The Shape of Generating Families

Ziqin Feng, Paul Gartside

The topology of a space $X$ is generated by a family $C$ of its subsets provided that a set $A \subseteq X$ is closed in $X$ if and only if $A \cap C$ is closed in $C$ for…

math.LO2024

Products of Directed Sets with Calibre $(ω_{1}, ω)$

Paul Gartside, Jeremiah Morgan

A directed set $P$ is calibre $(ω_{1}, ω)$ if every uncountable subset of $P$ contains an infinite bounded subset. $P$ is productively calibre $(ω_{1}, ω)$ if $P \times Q$ is calibre $…

math.GN2024

The Shape of Compact Covers

Ziqin Feng, Paul Gartside

For a space $X$ let $K (X)$ be the set of compact subsets of $X$ ordered by inclusion. A map $ϕ : K (X) \to K (Y)$ is a relative Tukey quotient if it carri…

math.GN2023

Directed Sets of Topology -- Tukey Representation and Rejection

Ziqin Feng, Paul Gartside

Every directed set is Tukey equivalent to (a) the family of all compact subsets, ordered by inclusion, of a (locally compact) space, to (b) a neighborhood filter, ordered by revers…

math.GN2021

Box and Nabla Products that are D-Spaces

Hector A. Barriga-Acosta, Paul M. Gartside

A space $X$ is $D$ if for every assignment, $U$ , of an open neighborhood to each point $x$ in $X$ there is a closed discrete $D$ such that $⋃ {U (x) : x \in D} = X$ . The box p…

The Cofinality of Generating Familes

The Shape of Generating Families

Products of Directed Sets with Calibre (ω1​,ω)

The Shape of Compact Covers

Directed Sets of Topology -- Tukey Representation and Rejection

Box and Nabla Products that are D-Spaces

Products of Directed Sets with Calibre $(ω_{1}, ω)$