The amalgamation of closure and boundary functions on semigroups and partially ordered sets. (English) Zbl 1078.06501

Shum, K. P.

Shum, K.P. (ed.) et al., Ordered structures and algebra of computer languages. Proceedings of the Southeast Asian Mathematical Society conference, Chinese University of Hong Kong, Hong Kong, June 26–29, 1991. River Edge, NJ: World Scientific (ISBN 981-02-1240-2/hbk). 232-243 (1993).

Summary: We show that the compositions of the boudary function with the complementary function, the interior function, the closure function and the rim function are all finitary in character. This result extends the well-known Kuratowski closure and complementation theorem in general topology.
For the entire collection see [Zbl 1061.20500].

MSC:

06A06	Partial orders, general
06A15	Galois correspondences, closure operators (in relation to ordered sets)
20M99	Semigroups