8 papers · 1 filter
On centered local -bases
Nathan Carlson
In 1967 Hajnal and Juh{á}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most , the cardinal…
Power homogeneous compacta and variations on tightness
Nathan Carlson
The weak tightness , introduced in [6], has the property . It was shown in [4] that if is a homogeneous compactum then . We intro…
A survey of cardinality bounds on homogeneous topological spaces
Nathan Carlson
In this survey we catalogue the many results of the past several decades concerning bounds on the cardinality of a topological space with homogeneous or homogeneous-like properties…
On weakening tightness to weak tightness
Angelo Bella, Nathan Carlson
The weak tightness of a space was introduced in [11] with the property . We investigate several well-known results concerning and consider whethe…
-H-closed spaces
Fortunata Aurora Basile, Maddalena Bonanzinga, Nathan Carlson +1
In this paper we extend the theory of H-closed extensions of Hausdorff spaces to a class of non-Hausdorff spaces, defined in \cite{B}, called -Hausdorff spaces. The notion of H-…
On cardinality bounds for -Urysohn spaces
Fortunata Aurora Basile, Nathan Carlson, Jack Porter
We introduce the class of -Urysohn spaces and the --closure operator. -Urysohn spaces generalize the notion of a Urysohn space. We estabilish bounds on the cardin…