reserve x,X,X2,Y,Y2 for set;
reserve GX for non empty TopSpace;
reserve A2,B2 for Subset of GX;
reserve B for Subset of GX;

theorem Th15:
  for A being Subset of GX, p being Point of GX st A is connected
  & p in A holds Component_of p=Component_of A
proof
  let A be Subset of GX, p be Point of GX;
  assume that
A1: A is connected and
A2: p in A;
  A c= Component_of A & Component_of A is a_component by A1,A2,Th1,Th8;
  hence thesis by A2,CONNSP_1:41;
end;
