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COUNTABLY COMPACT EXTENSIONS AND CARDINAL CHARACTERISTICS OF THE CONTINUUM
- Part of
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- Journal:
- The Journal of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 13 February 2025, pp. 1-27
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- Article
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In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance,
$\mathfrak b=\mathfrak s=\mathfrak c$ if and only if every regular first-countable space of weight 
$< \mathfrak c$ can be densely embedded into a regular first-countable countably compact space.
