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Every closed subset of a compact topological space is compact. Also every compact subset of a Hausdorff topological space is closed. It follows that compact subsets are precisely the closed subsets in a compact Hausdorff space. It is also proved that a topological space is maximal compact if and only if its compact subsets are precisely the closed subsets. A locale is a categorical extension of topological spaces and a frame is an object in its opposite category. We investigate to find whether the closed sublocales are exactly the compact sublocales of a compact Hausdorff frame. We also try to investigate whether the closed sublocales are exactly the compact sublocales of a maximal compact frame.
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참고문헌 (10)
참고문헌 신청
A. Ramanathan / 1948 / Minimal-bicompact spaces / J. Indian Math. Soc 12:40~46
B. Banaschewski / 1992 / Singly generated frame extensions / J.of Pure.Appl.Alg 83:1~21
C. H. Dowker / 1977 / Sums in the category of frames / Houston J.Math 3:7~15
Jayaprasad, P. N / 2012 / Reversible Frames / Journal of Advanced Studies in Topology 3(2):7~13
Jayaprasad. P. N / 2013 / On Singly Generated Extension of a Frame / Bulletin of the Allahabad Math. Soc 2(28):183~193
B. Banaschewski / 1992 / Singly generated frame extensions / J.of Pure.Appl.Alg 83:1~21
C. H. Dowker / 1977 / Sums in the category of frames / Houston J.Math 3:7~15
Jayaprasad, P. N / 2012 / Reversible Frames / Journal of Advanced Studies in Topology 3(2):7~13
Jayaprasad. P. N / 2013 / On Singly Generated Extension of a Frame / Bulletin of the Allahabad Math. Soc 2(28):183~193
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