The problem to embed a space into a first countable H-closed like space is considered. As a consequence, it is shown that no upper bound exists either for the cardinality of a first countable almost Lindelof space or for the cardinality of an H-set contained in a first countable Hausdorff space.
Embeddings into normal first countable spaces
β Scribed by Alessandro Fedeli; Attilio Le Donne
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 43 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0166-8641
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β¦ Synopsis
In this paper we construct, in response to a question of Arhangel'skiΗ, a zero-dimensional first countable space which cannot be embedded into a normal first countable space.
π SIMILAR VOLUMES
We show that it is consistent with the Continuum Hypothesis that first countable, countably compact spaces with no uncountable free sequences are compact. As a consequence, we get that CH does not imply the existence of a perfectly normal, countably compact, non-compact space, answering a question o
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