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Two More Hereditarily Separable Non-Lindelöf Spaces

Published online by Cambridge University Press:  20 November 2018

I. Juhász ,
K. Kunen  and
M. E. Rudin
I. Juhász
Affiliation:
University of Wisconsin, Madison, Wisconsin
K. Kunen
Affiliation:
University of Wisconsin, Madison, Wisconsin
M. E. Rudin
Affiliation:
University of Wisconsin, Madison, Wisconsin
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Our method using CH is a blend of two earlier constructions (Hajnal-Juhász [2] and Ostaszewski [4]) of hereditarily separable (HS), regular, non-Lindelöf, first countable spaces. [4] produces a much better space than ours in § 1 ; it has all of our properties except that it is not realcompact (which is probably more interesting), and it is countably compact as well; however, the construction works only under ◇, which implies the continuum hypothesis (CH) but is not equivalent to it.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 998 - 1005
Copyright
Copyright © Canadian Mathematical Society 1976

References

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