reserve a, r, s for Real;

theorem Th14:
  for T being non empty TopSpace, S being non empty open SubSpace
  of T st T is locally_connected holds S is locally_connected
proof
  let T be non empty TopSpace;
  let S be non empty open SubSpace of T;
  assume T is locally_connected;
  then the TopStruct of S is locally_connected by Lm10;
  hence thesis by Th12;
end;
