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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Products of sequentially compact spaces and the $ V$-process


Authors: M. Rajagopalan and R. Grant Woods
Journal: Trans. Amer. Math. Soc. 232 (1977), 245-253
MSC: Primary 54G20
MathSciNet review: 0451219
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Abstract: In this paper we produce a family of sequentially compact, locally compact, $ {T_2}$ 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, $ {T_2}$, sequentially compact space K which is not p-compact for any $ p \in \beta N - N$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0451219-7
PII: S 0002-9947(1977)0451219-7
Keywords: Scattered spaces, p-compact, countably compact, sequentially compact, $ \beta $N, quotients, partitions
Article copyright: © Copyright 1977 American Mathematical Society