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Pseudo-compact space

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A completely-regular space such that every real-valued continuous function on is bounded. In the class of normal spaces the concepts of countable compactness (cf. Countably-compact space) and pseudo-compactness coincide.


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References

[a1] R. Engelking, "General topology" , Heldermann (1989)
[a2] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) pp. 136 (Translated from Russian)
How to Cite This Entry:
Pseudo-compact space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-compact_space&oldid=11440
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article