Closed subsets in Bishop topological groups

We introduce the notion of a Bishop topological group i.e., X equipped with topology functions F such that operations are morphisms respect to F. A closed subset in neighborhood structure induced by its is defined positive way not as complement an open X. The corresponding closure operator, although it topological, classical sense, does involve sequences. As countable choice (CC) avoided, and agreement Richman's critique on use CC constructive mathematics, fundamental facts subsets groups shown here have clear algorithmic content. work within Bishop's informal system mathematics BISH, without choice, inductive definitions rules countably many premises.