Group of closure isomorphisms of Cech closure spaces

Abstract

Here we discuss some results on the group of all closure isomorphisms of a Cech closure space. A subgroup \(H\) of the symmetric group \(S(X)\) is \(c\) representable on $X$ if there exists a closure operator \(V\) on \(X\) such that the group of closure isomorphisms of the closure space \((X,\ V)\) is \(H\). In this paper, we prove a non trivial normal subgroup of the symmetric group \(S(X)\) is \(c\)-representable on \(X\) if and only if the cardinality of \(X\) is three.