Frames in which double pseudocomplements of cozero elements are cozero elements

Document Type : Research Paper

Authors

Department of Mathematical Sciences, College of Science, Engineering and Technology, University of South Africa, Johannesburg, South Africa

10.48308/cgasa.2026.243649.1606

Abstract

A Tychonoff space $X$ is said to be a CAP-space if the closure of the interior of every zero-set of $X$ is itself a zero-set of $X$. These spaces were introduced by Golrizkhatami and  Taherifar \cite{GT}. With a view to supplementing the results in the cited paper, we extend this notion to the setting of point-free topology. We thus define a completely regular frame to be capped in case the double pseudocomplement of every cozero element of the frame is also a cozero element. This   makes the comparison of this concept with other disconnectivity notions (such as basic disconnectedness) defined by imposing conditions on pseudocomplements very transparent. 
 

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