In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite. The concept was introduced by S. Mardeĉić and P. Papić in 1955. [1]
Some facts:
- Every compact space is feebly compact. [1]
- Every feebly compact paracompact space is compact.[ citation needed]
- Every feebly compact space is pseudocompact but the converse is not necessarily true. [1]
- For a completely regular Hausdorff space the properties of being feebly compact and pseudocompact are equivalent.[ citation needed]
- Any maximal feebly compact space is submaximal. [2]
References
- ^ a b c Hattori, Yasunao (20 May 2013). "THE WORK OF PROFESSOR KIYOSHI ISEKI ON TOPOLOGY". Scientiae Mathematicae Japonicae. 76 (2). Retrieved 26 September 2022.
- ^ Hrušák, Michael; Tkachenko, Mikhail; Tamariz-Mascarúa, Ángel, eds. (19 July 2018). Pseudocompact Topological Spaces: A Survey of Classic and New Results with Open Problems. Springer International Publishing. p. 193. Retrieved 26 September 2022.
 | This topology-related article is a stub. You can help Wikipedia by expanding it. |
In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite. The concept was introduced by S. Mardeĉić and P. Papić in 1955. [1]
Some facts:
- Every compact space is feebly compact. [1]
- Every feebly compact paracompact space is compact.[ citation needed]
- Every feebly compact space is pseudocompact but the converse is not necessarily true. [1]
- For a completely regular Hausdorff space the properties of being feebly compact and pseudocompact are equivalent.[ citation needed]
- Any maximal feebly compact space is submaximal. [2]
References
- ^ a b c Hattori, Yasunao (20 May 2013). "THE WORK OF PROFESSOR KIYOSHI ISEKI ON TOPOLOGY". Scientiae Mathematicae Japonicae. 76 (2). Retrieved 26 September 2022.
- ^ Hrušák, Michael; Tkachenko, Mikhail; Tamariz-Mascarúa, Ángel, eds. (19 July 2018). Pseudocompact Topological Spaces: A Survey of Classic and New Results with Open Problems. Springer International Publishing. p. 193. Retrieved 26 September 2022.
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| This topology-related article is a stub. You can help Wikipedia by expanding it. |