reserve T,U for non empty TopSpace;
reserve t for Point of T;
reserve n for Nat;
reserve T for TopStruct;
reserve f for PartFunc of R^1, T;
reserve c for Curve of T;
reserve T for non empty TopStruct;

theorem Th27:
  for c being with_endpoints Curve of T holds
  dom c = [.inf dom c, sup dom c.]
  proof
    let c be with_endpoints Curve of T;
    reconsider f = c as parametrized-curve PartFunc of R^1, T
    by Th23;
    dom f is interval Subset of REAL by Def4;
    then reconsider A = dom c as left_end right_end interval
    ext-real-membered set by Def6,Def7;
    A = [. min A, max A.]  by XXREAL_2:75;
    hence thesis;
  end;
