Representation of merotopic and nearness spaces
Let NEAR, MER, and PMER denote the categories of nearness spaces (in the sense of Herrlich), merotopic spaces, and premerotopic spaces (in the sense of Katĕtov). Then, in a natural way, NEAR\(\subset MER\subset PMER\). Moreover let BL be the category of base-lattices (e.g. see \textit{A. Pultr} and \textit{V. Trnková}, ``Combinatorial, algebraic and topological representations of groups, semigroups and categories'' (1980; Zbl 0418.18004). In this paper the categories NEL of nearness lattices, GRL of grill-lattices, and PGRL of pre-grill-lattices are introduced, and a pair G: PMER\(\to PGRL\) and M: PGRL\(\to PMER\) of functors is defined such that the following holds: (i) NEL\(\subset GRL\subset PGRL\subset BL\) (in a natural way); (ii) G is left adjoint to M; (iii) \(G| MER\) is left adjoint to \(M| GRL\); (iv) \(M| NEL\) is right adjoint to \(G| NEAR\).
scientific article; zbMATH DE number 4038776
scientific article