theorem Th97:
  for X0 being non empty SubSpace of X st the carrier of X0
  misses A for x0 being Point of X0 holds (modid(X,A))|X0 is_continuous_at x0
proof
  let X0 be non empty SubSpace of X;
  assume
A1: (the carrier of X0) /\ A = {};
  let x0 be Point of X0;
  x0 in the carrier of X0 & the carrier of X0 c= the carrier of X by BORSUK_1:1
;
  then reconsider x = x0 as Point of X;
  not x in A by A1,XBOOLE_0:def 4;
  hence thesis by Th58,Th96;
end;
