Abstract
A cozero sublocale C of a completely regular locale L will here be called coz-complemented if there is a cozero sublocale D of L such that \(C\cap D\) is the void sublocale and \(C\vee D\) is dense in L. Following terminology in spaces, we say L is a cloz-locale if every coz-complemented sublocale of L has an open closure. We characterize cloz-locales in terms of certain embeddings, and also in terms of ring-theoretic properties of the ring \({\mathcal {R}}L\) of real-valued continuous functions on L.
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The authors do wish to thank the referee for the insightful comments which have led to an improved presentation of this paper.
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Presented by Vincenzo Marra.
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The authors would also like to acknowledge funding from the Unisa Topology Research Chair that enabled Mugochi to visit Ighedo in June 2018, and enabled Ighedo to visit Mugochi in October 2018, during which periods most of the results in this paper were obtained.
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Ighedo, O., Mugochi, M.M. Locales whose coz-complemented cozero sublocales have open closures. Algebra Univers. 81, 17 (2020). https://doi.org/10.1007/s00012-020-00655-9
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DOI: https://doi.org/10.1007/s00012-020-00655-9