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pro vyhledávání: '"Gartside, Paul"'
Autor:
Gartside, Paul, Morgan, Jeremiah
A directed set $P$ is calibre $(\omega_1, \omega)$ if every uncountable subset of $P$ contains an infinite bounded subset. $P$ is productively calibre $(\omega_1, \omega)$ if $P \times Q$ is calibre $(\omega_1, \omega)$ for every directed set $Q$ wit
Externí odkaz:
http://arxiv.org/abs/2401.02603
Autor:
Feng, Ziqin, Gartside, Paul
For a space $X$ let $\mathcal{K}(X)$ be the set of compact subsets of $X$ ordered by inclusion. A map $\phi:\mathcal{K}(X) \to \mathcal{K}(Y)$ is a relative Tukey quotient if it carries compact covers to compact covers. When there is such a Tukey quo
Externí odkaz:
http://arxiv.org/abs/2401.00817
Autor:
Feng, Ziqin, Gartside, Paul
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 reverse inclusion, of a point (of a compact space, and of a topological grou
Externí odkaz:
http://arxiv.org/abs/2309.06523
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 $\bigcup \{U(x) : x \in D\}=X$. The box product, $\square X^\omega$, is $X^\omega$ with topology generated by a
Externí odkaz:
http://arxiv.org/abs/2111.10482
Roitman's combinatorial principle $\Delta$ is equivalent to monotone normality of the nabla product, $\nabla (\omega +1)^\omega$. If $\{ X_n : n\in \omega\}$ is a family of metrizable spaces and $\nabla_n X_n$ is monotonically normal, then $\nabla_n
Externí odkaz:
http://arxiv.org/abs/2006.15163
Autor:
Gartside, Paul, Pitz, Max
We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and K\"uhn with the topological theory of Eulerian continua defined as irreducible images of the
Externí odkaz:
http://arxiv.org/abs/1904.02645
Akademický článek
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Autor:
Gartside, Paul, Pitz, Max
A space $X$ is $n$-arc connected (respectively, $n$-circle connected) if for any choice of at most $n$ points there is an arc (respectively, a circle) in $X$ containing the specified points. We study $n$-arc connectedness and $n$-circle connectedness
Externí odkaz:
http://arxiv.org/abs/1807.02094
Given a graph G, of arbitrary size and unbounded vertex degree, denote by |G| the one-complex associated with $G$. The topological space |G| is n-arc connected (n-ac) if every set of no more than n points of |G| are contained in an arc (a homeomorphi
Externí odkaz:
http://arxiv.org/abs/1801.00179