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- W163985449 abstract "Discrete systems such as sets, monoids, groups are familiar categories. The internal strucutre of the latter two is dened by an algebraic operator. In this paper we describe the internal structure of the base set by a closure operator. We illustrate the role of such closure in convex geometries and partially ordered sets and thus suggest the wide applicability of closure systems. Next we develop the ideas of closed and complete functions over closure spaces. These can be used to establish criteria for asserting that the closure of a functional image under f is equal to the functional image of the closure. Functions with these properties can be treated as categorical morphisms. Finally, the category ClosureSys of closure systems is shown to be cartesian closed." @default.
- W163985449 created "2016-06-24" @default.
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- W163985449 date "2005-01-01" @default.
- W163985449 modified "2023-09-27" @default.
- W163985449 title "A Category of Discrete Closure Systems" @default.
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