On relatively connected sublocales and J-frames

Articles in Press

Document Type : Research Paper

Authors

School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa.

10.48308/cgasa.2024.235270.1481

Abstract

In this paper, we present a study of relatively connected sublocales. Connected sublocales are relatively connected, not conversely. We study conditions under which relatively connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call C-normal frames. We show that normal frames are C-normal but not conversely. Some results concerning J-frames are presented; amongst other things, we prove that regular continuous frames are rim-compact. A rim-compact J-frame is regular continuous. The latter is used to show that the least compactification of a regular continuous J-frame coincides with its Freudenthal compactification. In turn, this contributes to the known conditions under which the least compactification is perfect.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 05 September 2024

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