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On locales whose countably compact sublocales have compact closure

Themba Dube (2023)

Mathematica Bohemica

Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called cl -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.

On minimal ideals in the ring of real-valued continuous functions on a frame

Abolghasem Karimi Feizabadi, Ali Akbar Estaji, Mostafa Abedi (2018)

Archivum Mathematicum

Let L be the ring of real-valued continuous functions on a frame L . The aim of this paper is to study the relation between minimality of ideals I of L and the set of all zero sets in L determined by elements of I . To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame L , it is proved that the f -ring L is isomorphic to the f -ring C ( Σ L ) of all real continuous functions on the topological space Σ L . Finally, a one-one correspondence is...

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