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# pseudocompact space

A topological space $X$ is said to be *pseudocompact* if every continuous function $f\colon X\to\mathbb{R}$ has bounded image.

All countably compact spaces (which includes all compact spaces and all sequentially compact spaces) are pseudocompact. A metric space is pseudocompact if and only if it is compact. A Hausdorff normal space is pseudocompact if and only if it is countably compact.

Defines:

pseudocompact, pseudocompactness, pseudo-compact, pseudo-compactness, pseudo compact, pseudo compactness

Related:

LimitPointCompact

Synonym:

pseudo compact space, pseudo-compact space

Type of Math Object:

Definition

Major Section:

Reference

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54D30*no label found*

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier