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-bitightness small number of a space X, btsθ(X), and prove that in every topological space X, the cardinality of the θ-closed hull of each set A is at most |A|btsθ(X). Using this result, we synthesize all earlier results on bounds on the cardinality of θ-closed hulls. We provide applications to P-spaces and to the almost-Lindelöf number. © 2013 Elsevier B.V.
On the cardinality of the θ-closed hull of sets / Cammaroto, F.; Catalioto, A.; Pansera, B. A.; Tsaban, B.. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 160:18(2013), pp. 2371-2378. [10.1016/j.topol.2013.07.031]
On the cardinality of the θ-closed hull of sets
Pansera B. A.;
2013-01-01
Abstract
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-bitightness small number of a space X, btsθ(X), and prove that in every topological space X, the cardinality of the θ-closed hull of each set A is at most |A|btsθ(X). Using this result, we synthesize all earlier results on bounds on the cardinality of θ-closed hulls. We provide applications to P-spaces and to the almost-Lindelöf number. © 2013 Elsevier B.V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
