Almost disjoint families and relative versions of covering properties of κ-paracompactness type
| Autor: | Dimi R. Rangel, Samuel G. da Silva, Charles Morgan |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
010102 general mathematics 02 engineering and technology Disjoint sets Type (model theory) Space (mathematics) 01 natural sciences Combinatorics Disjoint union (topology) 0202 electrical engineering electronic engineering information engineering Countable set 020201 artificial intelligence & image processing Geometry and Topology General topology Set theory Paracompact space 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 221:476-490 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2017.02.031 |
| Popis: | This paper is an enlarged, revised and improved version of a poster presented by the second author at the 2013 Brazilian Conference on General Topology and Set Theory (STW 2013, Maresias, Brazil, 2013). Our main goal is to investigate – within the realm of Isbell–Mrowka spaces – some relative versions of covering properties of κ-paracompactness type, inspired by a comprehensive list of strengthenings of countable paracompactness introduced by M.E. Rudin in [18] . For any property P among the ones presented, we will say that an almost disjoint family A satisfies P if it satisfies a relative version of P in the corresponding Isbell–Mrowka space. We present combinatorial characterizations of the a.d. families with some of these new relative topological properties and prove several related results; for instance, it is shown that maximal almost disjoint families are not countably paracompact. The paper finishes with a number of questions and open problems. |
| Databáze: | OpenAIRE |
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