On maximal compact frames
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초록
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.
Abstract
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.
참고문헌 (10)
- A. Ramanathan, "Minimal-bicompact spaces", J. Indian Math. Soc, 12, pp.40~46 (1948)
- B. Banaschewski, "Singly generated frame extensions", J.of Pure.Appl.Alg, 83, pp.1~21 (1992)
- C. H. Dowker, "Sums in the category of frames", Houston J.Math, 3, pp.7~15 (1977)
- Jayaprasad, P. N, "Reversible Frames", Journal of Advanced Studies in Topology, 3(2), pp.7~13 (2012)
- Jayaprasad. P. N, "On Singly Generated Extension of a Frame", Bulletin of the Allahabad Math. Soc, 2(28), pp.183~193 (2013)
- J. Paseka., "T2 Frames and Almost compact frames", Czech. Math. J, 42, pp.385~402 (1992)
- J.Picado, "Frames and Locales-Topology without Points" (2012), Birkhauser
- J. R. Isbell, "Atomless parts of spaces", Math.Scand, 31, pp.5~32 (1972)
- N. Levine, "When are compact and closed equivalent?", Amer.Math.Month, 1(71), pp.41~44 (1965)
- P. T. Johnstone, "Cambridge Studies in Advanced Mathematics 3" (1982), Camb.Univ.Press