Topology inside $\omega_1$
| Autor: | David Lutzer, Harold Bennett |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Lemma (mathematics)
pressing down lemma General Mathematics 54B10 Disjoint sets Topology $\omega_1$ stationary set Borel measure countable ordinals products of stationary sets 54F05 54G15 03E10 Metrization theorem Stationary set Product topology club-set Ulam Matrix Club set Topology (chemistry) Borel sets Borel measure Mathematics |
| Zdroj: | Rocky Mountain J. Math. 50, no. 6 (2020), 1989-2000 |
| Popis: | In this expository paper, we show how the pressing down lemma and Ulam matrices can be used to study the topology of subsets of [math] . We prove, for example, that if [math] and [math] are stationary subsets of [math] with [math] stationary, then [math] and [math] cannot be homeomorphic. Because Ulam matrices provide [math] -many pairwise disjoint stationary subsets of any given stationary set, it follows that there are [math] -many stationary subsets of any stationary subset of [math] with the property that no two of them are homeomorphic to each other. We also show that if [math] and [math] are stationary sets, then the product space [math] is normal if and only if [math] is stationary. In addition, we prove that for any [math] , [math] is normal, and that if [math] is hereditarily normal, then [math] is metrizable. |
| Databáze: | OpenAIRE |
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