Closures and topological closures in quasi-discrete closure spaces

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Abstract

Closure space was introduced by Cech as a generalization of ordinary topology. In this work we establish a one to one correspondence between quasi-discrete closures and reflexive relations. We show that, in a quasi-discrete closure space, if a closure cl and its topological closure clT are respectively generated by relations R and S, then S is the transitive closure of R.

Keywords

Closures
Topological closure
Quasi-discrete closures
Binary relations
Boolean matrices
Transitive closure

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Partially supported by the National Natural Science Foundation of China (No. 60973148) and the Key Project of the Chinese Ministry of Education (No. 108133).