pseudocompact space

A topological spaceMathworldPlanetmath X is said to be pseudocompact if every continuous functionMathworldPlanetmath f:X has boundedPlanetmathPlanetmathPlanetmathPlanetmath 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 compactPlanetmathPlanetmath. A HausdorffPlanetmathPlanetmath normal spaceMathworldPlanetmath is pseudocompact if and only if it is countably compact.

Title pseudocompact space
Canonical name PseudocompactSpace
Date of creation 2013-03-22 14:20:36
Last modified on 2013-03-22 14:20:36
Owner yark (2760)
Last modified by yark (2760)
Numerical id 7
Author yark (2760)
Entry type Definition
Classification msc 54D30
Synonym pseudo compact space
Synonym pseudo-compact space
Related topic LimitPointCompact
Defines pseudocompact
Defines pseudocompactness
Defines pseudo-compact
Defines pseudo-compactness
Defines pseudo compact
Defines pseudo compactness