proposition: Lemma connected1 x : connected [set x].
proof: Proof. move=> X [y +] [O Oopen XO] [C Cclosed XC]; rewrite XO. by move=> [{y}-> Ox]; apply/seteqP; split=> y => [[->//]|->]. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed