Nearness, subfitness and sequential regularity
In the point-free context, the structure of nearness has been studied so far only in the regular case. The authors are concerned with the question as to how far beyond regularity one can go, that is, what is the weakest separation property under which an admissible nearness makes a reasonable sense. The answer is subfitness. Main theorem: The following statements on a frame \(L\) are equivalent: (i) Each sublocale of \(L\) quasi-admits a nearness; (ii) \(L\) is hereditarily subfit; (iii) \(L\) is sequentially regular; (iv) Each congruence on \(L\) is uniquely determined by the class containing 1. Finally, the authors compare the sequential regularity with more common separation axioms.
scientific article; zbMATH DE number 1563337