Abstract
Every collectionwise Hausdorff (CWT2) first countable space is regular. Generalizations of first countability are considered. If X is hereditarily CWT2(HCWT2), blobular, of character N1, and contains no first countable S space, then X is regular. The existence of a first countable S space implies the existence of a nonregular, HCWT2, lob space of character N1. If it is consistent that there are no HCWT2 analogues of S spaces for all regular ordinals τ, then the following is consistent. Every HCWT2 globular space is regular.
AMS (MOS) subject classification (1980)
- Primary 54A25
- 54D10
- 54D15
- Secondary 54A35
- 54E99
- Key words and phases
- Hereditarily collectionwise Hausdorff
- regularity
- lob
- blobular
- globular
- S space
- right separated
- scattered
The second author is pleased to thank the International Research and Exchanges Board and the Hungarian Academy of Science for Support during the preparation of this paper.
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© 1989 Springer-Verlag
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Nagy, Z., Purisch, S. (1989). When hereditarily collectionwise Hausdorffness implies regularity. In: Steprāns, J., Watson, S. (eds) Set Theory and its Applications. Lecture Notes in Mathematics, vol 1401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097336
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DOI: https://doi.org/10.1007/BFb0097336
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