13 papers
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…
On n-Hausdorff homogeneous and n-Urysohn homogeneous spaces
Maddalena Bonanzinga, Nathan Carlson, Davide Giacopello +1
In this paper we study -Hausdorff homogeneous and -Urysohn homogeneous spaces. We give some upper bounds for the cardinality of these kind of spaces and give examples. Additi…
New bounds on the cardinality of n-Hausdorff and n-Urysohn spaces
Maddalena Bonanzinga, Nathan Carlson, Davide Giacopello
Two new cardinal functions defined in the class of -Hausdorff and -Urysohn spaces that extend pseudocharacter and closed pseudocharacter respectively are introduced. Through…
New bounds on the cardinality of Hausdorff spaces and regular spaces
Nathan Carlson
Using weaker versions of the cardinal function , we derive a series of new bounds for the cardinality of Hausdorff spaces and regular spaces that do not involve no…
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…
Variations on known and recent cardinality bounds
Fortunata Aurora Basile, Maddalena Bonanzinga, Nathan Carlson
Sapirovskii [18] proved that , for a regular space . We introduce the -pseudocharacter of a Urysohn space , denoted by , and prove that th…
On the weak tightness, Hausdorff spaces, and power homogeneous compacta
Nathan Carlson
Motivated by results of Juhász and van Mill in [13], we define the cardinal invariant , the weak tightness of a topological space , and show that $|X|\leq 2^{L(X)wt(X)ψ(X…
On the cardinality of Hausdorff spaces and H-closed spaces
Nathan Carlson, Jack Porter
We introduce the cardinal invariant and show that for any Hausdorff space (a corollary of Theorem 4.4. This invariant has the prop…
Cardinality bounds involving the skew- Lindelöf degree and its variants
Nathan Carlson, Jack Porter
We introduce a modified closing-off argument that results in several improved bounds for the cardinalities of Hausdorff and Urysohn spaces. These bounds involve the cardinal invari…