arXiv subjects

Andrei Catalioto

Publications and source records attributed to Andrei Catalioto.

5 recordsLinked to original sources

arXiv2012

On the cardinality of the $θ$-closed hull of sets II

The research in this paper is a continuation of the investigation of the cardinality of the $θ$-closed hull of subsets of spaces. This research obtains new upper bounds of the cardinality of the $θ$-closed hull of subsets using cardinal functions of $θ$-bitightness (\cite{Ca-Ko}), finite $θ$-bitightness (\cite{Ca-Ca-Pa-Ts}) and $θ$-bitightness small number (\cite{Ca-Ca-Pa-Ts}) of spaces. In the final section, examples of spaces are presented including one that answers a question posed in \cite{Bo-Ca-Ma} and \cite{Bo-Pa}.

math.GN↗

arXiv2012

Cardinal functions $F_θ(X)$ and $t_θ(X)$ for H-closed spaces

In this article, starting with results from a paper by Cammaroto and Kočinac in 1993, we prove that $t_θ(X) = t_θ(X_{s}) = t(X_{s}) = F_θ(X) = F_θ(X_{s}) = F(X_{s})$ for every H-closed and Urysohn space and we present some useful examples to study the full relationships among the cardinal functions $t$, $t_θ$, $F$ and $F_θ$ in the context of H-closed and Urysohn spaces. Also, we construct an H-closed space $H$ for which $F_θ(H) < t_θ(H)$. Two questions posed by Cammaroto and Kočinac about H-closed spaces are answered.

math.GN↗

arXiv2012

Absolutes of Hausdorff spaces and cardinal invariants $F_{\te}$ and $t_{\te}$}

This article extends the recent study of the cardinal functions $F_θ$ and $t_θ$ for H-closed Urysohn spaces and the research of I. Bandlov and V.I. Ponomarev on tightness type of absolutes. In particular, basic results are obtained and used to study the relationships among the cardinal functions $t$, $t_θ$, $F$ and $F_θ$ in the context of Iliadis and Banaschewski absolutes of Hausdorff spaces.

math.GN↗

arXiv2012

On the cardinality of Hausdorff spaces

A common generalization for two of the main streams of cardinality inequalities is developed; each stream derives from the famous inequality established by A.V. Arhangel'ski\uı in 1969 for Hausdorff spaces. At the end of one stream is the recent inequality by Bella and at the end of the second stream is the 1988 inequality by Bella and Cammaroto. This generalization is extended and used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality. The paper is concluded with some open problems.

math.GN↗

arXiv2012

On the cardinality of the $θ$-closed hull of sets

The θ-closed hull of a set A in a topological space is the smallest set C containing A such that, whenever all $closed$ neighborhoods of a point intersect C, this point is in C. We define a new topological cardinal invariant function, the $θ-bitighness small number$ of a space X, bts_theta(X), and prove that in every topological space X, the cardinality of the theta-closed hull of each set A is at most |A|^{bts_theta(X)}. Using this result, we synthesize all earlier results on bounds on the cardinality of theta-closed hulls. We provide applications to P-spaces and to the almost-Lindelof number.

math.GN↗