Representation of merotopic and nearness spaces
type: Item
instance of: scholarly article
title: Representation of merotopic and nearness spaces
zbMATH Open document ID: 0637.54023
DOI: 10.1016/0166-8641(88)90039-9
author: Wolfgang Weiss
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: 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 \(G| NEAR\).
reviewed by: Harald Brandenburg
Mathematics Subject Classification ID: 54E17
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 4038776
zbMATH Keywords: nearness spaces
zbMATH Keywords: merotopic spaces
zbMATH Keywords: premerotopic spaces
zbMATH Keywords: base-lattices
zbMATH Keywords: nearness lattices
zbMATH Keywords: grill-lattices
zbMATH Keywords: pre-grill-lattices
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90039-9
OpenAlex ID: W2055831495
cites work: Q3222241
cites work: Q3898534
cites work: Topological functors
cites work: A concept of nearness
cites work: Q3968115
cites work: Q5682456
cites work: Q5511986
cites work: On the scale of a uniform space
cites work: Q3670150
cites work: Free Completely Distributive Lattices
cites work: Q3208855
cites work: Q3890747
cites work: On Wyler's Taut lift theorem
description: scientific article; zbMATH DE number 4038776