Korean J. Math.  Vol 29, No 3 (2021)  pp.493-499
DOI: https://doi.org/10.11568/kjm.2021.29.3.493

On maximal compact frames

Jayaprasad P N, Madhavan Namboothiri N M, Santhosh P K, Varghese Jacob

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. 


Keywords


Frame, locale, spatial frame, maximal compact frame, subframe, sublocale.

Subject classification

06D22, 54E

Sponsor(s)



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