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

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17 papers · 1 filter

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.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…

math.GN2020

Monotone Normality and Nabla-Products

Hector A. Barriga-Acosta, Paul M. Gartside

Roitman's combinatorial principle $Δ$ is equivalent to monotone normality of the nabla product, $\nabla (ω + 1)^{ω}$ . If ${X_{n} : n \in ω}$ is a family of metrizable spaces and $\nabl…

math.GN2019

Eulerian Spaces

Paul Gartside, Max Pitz

We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and Kühn with the topologi…