| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Citta Univ Catania, Univ Catania, Dept Math & Comp Sci, Viale A Doria 6, I-95125 Catania - Italy
[2] York Univ, Fac Sci & Engn, Dept Math, Toronto, ON M3J 1P3 - Canada
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | ACTA MATHEMATICA HUNGARICA; v. 154, n. 1, p. 252-263, FEB 2018. |
| Web of Science Citations: | 4 |
| Abstract | |
We solve a long standing question due to Arhangel'skii by constructing a compact space which has a cover with no continuum-sized ()-dense subcollection. We also prove that in a countably compact weakly Lindelof normal space of countable tightness, every cover has a -sized subcollection with a -dense union and that in a Lindelof space with a base of multiplicity continuum, every cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De la Vega's celebrated theorem on the cardinality of homogeneous compacta of countable tightness. (AU) | |
| FAPESP's process: | 13/14640-1 - Discrete sets and cardinal invariants in set-theoretic topology |
| Grantee: | Santi Domenico Spadaro |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |