A separable space with no remote points

Author:
Alan Dow

Journal:
Trans. Amer. Math. Soc. **312** (1989), 335-353

MSC:
Primary 54D35; Secondary 03E35, 03E55, 54A35, 54D40, 54D60

DOI:
https://doi.org/10.1090/S0002-9947-1989-0983872-1

MathSciNet review:
983872

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In the model obtained by adding side-by-side Sacks reals to a model of , there is a separable nonpseudocompact space with no remote points. To prove this it is also shown that in this model the countable box product of Cantor sets contains a subspace of size such that every uncountable subset has density . Furthermore assuming the existence of a measurable cardinal with , a space is produced with no isolated points but with remote points in . It is also shown that a pseudocompact space does not have remote points.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0983872-1

Keywords:
Remote points,
measurable cardinals,
side-by-side Sacks forcing

Article copyright:
© Copyright 1989
American Mathematical Society