The weight of a pseudocompact (homogeneous) space whose cardinality has countable cofinality

Author:
Eric K. van Douwen

Journal:
Proc. Amer. Math. Soc. **80** (1980), 678-682

MSC:
Primary 54A25

DOI:
https://doi.org/10.1090/S0002-9939-1980-0587954-5

MathSciNet review:
587954

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *X* be an infinite pseudocompact space. We are interested in restrictions on and in addition to the obvious inequalities and and , valid for *X* without isolated points (in particular for homogeneous *X*). We show that if then , and even for some if *X* is homogeneous. Under the Singular Cardinals Hypothesis (which is much weaker than the GCH), there are no further restrictions for *X* without isolated points.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0587954-5

Keywords:
Weight,
cardinality,
countably cofinality,
strong limit,
pseudocompact,
homogeneous

Article copyright:
© Copyright 1980
American Mathematical Society