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Cellularity of first countable spaces

✍ Scribed by Juris Steprāns; Stephen Watson


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
275 KB
Volume
28
Category
Article
ISSN
0166-8641

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CH and first countable, countably compac
✍ Todd Eisworth 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 157 KB

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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In this paper we construct, in response to a question of Arhangel'skiǐ, a zero-dimensional first countable space which cannot be embedded into a normal first countable space.