Some relations between prime inner operators, prime closure operators and connections. (Chinese. English summary) Zbl 1424.06010

Xu, Kuankuan; Lu, Tao

J. Jiangsu Norm. Univ., Nat. Sci. 36, No. 3, 57-58, 68 (2018).

Summary: Some relations between prime inner operators, prime closure operators and Galois connections have been studied. Some main conclusions about the relations of them are obtained: 1) the sufficient condition for \((f, g)\) to be a Galois connection, when \(f\) is a prime inner operator, \(g\) is a prime closure operator, is that \(f\) and \(g\) have the same fixed point sets; 2) under certain conditions, if \((f, g)\) is Galois connection, then \(gf\) is a prime closure operator and \(fg\) is a prime inner operator.

MSC:

06A15	Galois correspondences, closure operators (in relation to ordered sets)
54A05	Topological spaces and generalizations (closure spaces, etc.)

Keywords:

prime inner operator; prime closure operator; connection