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.
| Original language | English |
|---|---|
| Pages (from-to) | 2371-2378 |
| Number of pages | 8 |
| Journal | Topology and its Applications |
| Volume | 160 |
| Issue number | 18 |
| DOIs | |
| State | Published - 1 Dec 2013 |
Bibliographical note
Funding Information:This research was partially supported by CNR (GNSAGA) and MIUR , Italy, through “Fondi 40%”. A part of this work was carried out during a visit of the fourth named author at the University of Messina. This author thanks his hosts for their warm hospitality and stimulating atmosphere.
Funding
This research was partially supported by CNR (GNSAGA) and MIUR , Italy, through “Fondi 40%”. A part of this work was carried out during a visit of the fourth named author at the University of Messina. This author thanks his hosts for their warm hospitality and stimulating atmosphere.
| Funders | Funder number |
|---|---|
| Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni | |
| Ministero dell’Istruzione, dell’Università e della Ricerca | |
| Consiglio Nazionale delle Ricerche |
Keywords
- Cardinal inequalities
- Character
- Finite θ-bitightness
- Finitely-Urysohn space
- H-closed space
- H-set
- N-Urysohn space
- Urysohn number
- Urysohn space
- θ-Bitightness
- θ-Bitightness small number
- θ-Character
- θ-Closed hull
- θ-Closure
- θ-Tightness