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A compact space having the cardinality of the continuum with no convergent sequences

Published online by Cambridge University Press:  24 October 2008

V. V. Fedorčuk
V. V. Fedorčuk
Affiliation:
Mechanics and Mathematical Faculty; Moscow University, USSR
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Extract

1. Introduction. All spaces in this paper are Hausdorff. We recall that a space X is sequentially compact, if every countable subset of X contains a convergent sequence. Let us consider the three statements:

(1) Every compact space of cardinality ≤ ʗ contains a point of countable character.

(2) Every compact space of cardinality ≤ ʗ is sequentially compact.

(3) Every infinite compact space of cardinality ≤ ʗ contains a convergent sequence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 177 - 181
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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