There are many Ostaszewski spaces

LaBerge, Timothy J.

doi:10.1090/S0002-9939-1993-1137225-2

There are many Ostaszewski spaces
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by Timothy J. LaBerge PDF

Proc. Amer. Math. Soc. 118 (1993), 987-993 Request permission

Abstract:

We show that ${\diamondsuit _{{\omega _1}}}$ implies there is a family of ${2^{{\omega _1}}}$ many pairwise nonhomeomorphic Ostaszewski spaces, with the additional property that any continuous image of one in another is compact. We also present diamond versions of Fleissner’s forcing results concerning the normality of products of Ostaszewski spaces and their compactifications.

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