×

A constructive Galois connection between closure and interior. (English) Zbl 1275.03161

It is known that the theory of closure operators and that of interior operators can be derived from one another. In the paper under review the authors construct a Galois connection between closure and interior operators on a given set. Generally, all arguments are intuitionistically valid. The construction made by the authors in this paper is an intuitionistic version of the classical correspondence between closure and interior operators via complement. A Galois connection between saturation and reduction is also studied in this paper.

MSC:

03F55 Intuitionistic mathematics
06A15 Galois correspondences, closure operators (in relation to ordered sets)
PDFBibTeX XMLCite
Full Text: DOI arXiv Euclid

References:

[1] Categories for the working mathematician (1998) · Zbl 0906.18001
[2] Memoirs of the American Mathematical Society 51 (1984)
[3] Stone spaces 3 (1983)
[4] DOI: 10.2307/2372123 · Zbl 0045.31505 · doi:10.2307/2372123
[5] DOI: 10.1002/malq.19830290103 · Zbl 0521.03045 · doi:10.1002/malq.19830290103
[6] Sheaves and logic, Applications ofsheaves. Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, July 21, 1977 753 (1979)
[7] DOI: 10.1016/S0304-3975(02)00704-1 · Zbl 1044.54001 · doi:10.1016/S0304-3975(02)00704-1
[8] Formal topologies on the set of first-order formulae 65 pp 1183– (2000) · Zbl 0965.03072
[9] DOI: 10.1016/j.jpaa.2010.02.002 · Zbl 1192.03047 · doi:10.1016/j.jpaa.2010.02.002
[10] Annals of Pure and Applied Logic
[11] Lattice theory 25 (1940)
[12] From sets and types to topology and analysis: towards practicable foundations for constructive mathematics 48 pp 176– (2005)
[13] The basic picture and positive topology. New structures for constructive mathematics
[14] DOI: 10.1016/S0168-0072(03)00052-6 · Zbl 1070.03041 · doi:10.1016/S0168-0072(03)00052-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.