Products of sequentially compact spaces and the -process

Authors:
M. Rajagopalan and R. Grant Woods

Journal:
Trans. Amer. Math. Soc. **232** (1977), 245-253

MSC:
Primary 54G20

DOI:
https://doi.org/10.1090/S0002-9947-1977-0451219-7

MathSciNet review:
0451219

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we produce a family of sequentially compact, locally compact, first countable, scattered and separable spaces whose product is not countably compact and thus answer a problem of C. T. Scarborough and A. H. Stone [11] in the negative. We do this using the continuum hypothesis. We also produce a completely regular, , sequentially compact space *K* which is not *p*-compact for any .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1977-0451219-7

Keywords:
Scattered spaces,
*p*-compact,
countably compact,
sequentially compact,
*N*,
quotients,
partitions

Article copyright:
© Copyright 1977
American Mathematical Society