# Difference between revisions of "Pseudo-compact space"

From Encyclopedia of Mathematics

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

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− | + | |valign="top"|{{Ref|ArPo}}||valign="top"| A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises", Reidel (1984) pp. 136 (Translated from Russian) | |

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− | + | |valign="top"|{{Ref|En}}||valign="top"| R. Engelking, "General topology", Heldermann (1989) | |

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## Latest revision as of 22:31, 2 May 2012

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.

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Pseudo-compact_space&oldid=25858

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article