Pseudo-compact space

From Encyclopedia of Mathematics
Jump to: navigation, search

2010 Mathematics Subject Classification: Primary: 54D30 [MSN][ZBL]

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


[ArPo] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises", Reidel (1984) pp. 136 (Translated from Russian)
[En] R. Engelking, "General topology", Heldermann (1989)
How to Cite This Entry:
Pseudo-compact space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article