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Variants of Compactness in Pointfree Topology

Bernhard Banaschewski|Sung Sa Hong
경북대학교 자연과학대학 수학과|2005.12|Kyungpook Mathematical Journal|제45권 제4호|pp. 455-470

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Abstract

This paper introduces compactnessnotions forframeswhich areexpressedintermsofthe convergenceofsuitably specied general lters.It establishesseveral preser-vation propertiesforthem as well as theircoreectivenessin the settingofregularframes.Further,it shows that supercompact,compact,and Lindelof framescan be described bycompactnessconditions of the present formso that various familiarfactsbecome conse-quences of these general results.In addition, the Prime Ideal Theorem and the AxiomofCountable Choice are proved to be equivalent to certainconditions connected with thekind ofcompactnessconsidered here.

참고문헌 (16)

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관련 논문AI추천

General Filters and Strict Extensions in Pointfree TopologyBernhard Banaschewski, Sung Sa Hong경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제2호On Spaces in which compact-like sets are closed, and related spaces홍우철대한수학회 · 대한수학회논문집2007 · 제22권 제2호Remarks on $\mathcal K$-starcompact spacesYan-Kui Song대한수학회 · 대한수학회논문집2007 · 제22권 제4호Selection principles and hyperspace topologies in closure spacesMila Mr\v sevi\'c, Milena Jeli\'c대한수학회 · 대한수학회지2006 · 제43권 제5호Isocompactness and related topics of weak covering property조명현, Won Woo Park대한수학회 · 대한수학회보2002 · 제39권 제2호κ-Compact FramesNIZAR MARCUS경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제1호

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