Unions of chains in dyadic compact spaces and topological groups
| Autor: | Yolanda Torres Falcón, Mikhail Tkachenko |
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| Rok vydání: | 2002 |
| Předmět: |
Discrete mathematics
Regular cardinal Countably compact Mathematics::General Topology Totally bounded space Stationary set Locally compact group σ-compact Precompact Combinatorics Dyadic compact space Relatively compact subspace Metrization theorem Metrizable Countable set Increasing chain of subsets Geometry and Topology Topological group Locally compact space Mathematics |
| Zdroj: | Topology and its Applications. 121:25-32 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/s0166-8641(01)00106-7 |
| Popis: | The following problem is considered: If a topological group G is the union of an increasing chain of subspaces and certain cardinal invariants of the subspaces are known, what can be said about G? We prove that if G is locally compact and every subspace in the chain has countable pseudocharacter or tightness, then G is metrizable. We also prove a similar assertion for σ-compact and totally bounded groups represented as the union of first countable subspaces, when the length of the chain is a regular cardinal greater than ω1. Finally, we show that these results are not valid in general, not even for compact spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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