Remarks on monotone (weak) Lindelöfness
| Autor: | Maddalena Bonanzinga, Filippo Cammaroto, Masami Sakai |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
010102 general mathematics Monotonic function Space (mathematics) 01 natural sciences 010101 applied mathematics Combinatorics Monotone polygon Cardinality Caliber Lindelöf space Countable set Uncountable set Geometry and Topology 0101 mathematics Erdös–Rado Monotonically Lindelöf Monotonically weakly Lindelöf Pixley–Roy Mathematics |
| Zdroj: | Topology and its Applications. 225:195-205 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2017.04.009 |
| Popis: | Using Erdos–Rado's theorem, we show that (1) every monotonically weakly Lindelof space satisfies the property that every family of cardinality c + consisting of nonempty open subsets has an uncountable linked subfamily; (2) every monotonically Lindelof space has strong caliber ( c + , ω 1 ) , in particular a monotonically Lindelof space is hereditarily c -Lindelof and hereditarily c -separable. (1) gives an answer of a question posed in Bonanzinga, Cammaroto and Pansera [3] , and (2) gives partial answers of questions posed in Levy and Matveev [15] . Some other properties on monotonically (weakly) Lindelof spaces are also discussed. For example, we show that the Pixley–Roy space P R ( X ) of a space X is monotonically Lindelof if and only if X is countable and every finite power of X is monotonically Lindelof. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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