Feebly compact space
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Short description: Mathematics concept
In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite. The concept was introduced by Sibe Mardešić and P. Papić in 1955.[1]
Some facts:
- Every compact space is feebly compact.[1]
- Every feebly compact space is pseudocompact but the converse is not necessarily true.[1]
- Any maximal feebly compact space is submaximal.[2]
References
- ↑ 1.0 1.1 1.2 Hattori, Yasunao (20 May 2013). "THE WORK OF PROFESSOR KIYOSHI ISEKI ON TOPOLOGY". Scientiae Mathematicae Japonicae 76 (2). https://www.jstage.jst.go.jp/article/isms/76/2/76_299/_pdf. 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. ISBN 978-3-319-91680-4. https://books.google.com/books?id=fsRlDwAAQBAJ&dq=Any+maximal+feebly+compact+space+is+submaximal&pg=PA193. Retrieved 26 September 2022.
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