fact: Definition connected A := forall B, B !=set0 -> (exists2 C, open C & B = A `&` C) -> (exists2 C, closed C & B = A `&` C) -> B = A.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed