On the cardinality of the $\theta$-closed hull of sets

Autor:	Cammaroto, Filippo, Catalioto, Andrei, Pansera, Bruno Antonio, Tsaban, Boaz
Rok vydání:	2012
Předmět:	Mathematics - General Topology
Druh dokumentu:	Working Paper
Popis:	The \theta-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 $\theta-bitighness small number$ 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. Comment: Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1203.5824 Zobrazit plný text záznamu View this record from Arxiv