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Zbl 0882.18003
Adamek, Jiří; Pedicchio, M.-C.
A remark on topological spaces, grids, and topological systems. (English)
[J] Cah. Topologie Géom. Différ. Catég. 38, No.3, 217-226 (1997). ISSN 0008-0004

{\it M. Barr} and {\it M. C. Pedicchio} have shown that the category ${\cal T}op$ of topological spaces is dually equivalent to a quasivariety of abstract algebras (called grids) [same Cah. 36, No. 1, 3-10 (1995; Zbl 0819.18002)]. The authors of this paper now show that ${\cal T}op^{\text{op}}$ is embeddable in the comma-category of complete atomic Boolean algebras in frames, which are two-sorted algebras, with the image forming a subquasivariety. Also the variety of all grids is dually equivalent to {\it S. Vickers}' category of topological systems [``Topology via logic'' (1989; Zbl 0668.54001)].
[J.R.Isbell (Buffalo)]

MSC 2000:: *18B30 Categories of topological spaces
08C99 Classes of algebras
18C10 Algebraic theories, etc.

Keywords: grid; two-sorted algebra; topological system

Citations: Zbl 0819.18002; Zbl 0668.54001

Cited in: Zbl 0936.18004

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