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

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
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