reserve GX for TopSpace;
reserve A, B, C for Subset of GX;
reserve TS for TopStruct;
reserve K, K1, L, L1 for Subset of TS;
reserve GX for non empty TopSpace;
reserve A, C for Subset of GX;
reserve x for Point of GX;

theorem
  for T being TopSpace, X being Subset of T, Y being Subset of the
  TopStruct of T st X=Y holds X is a_component iff Y is a_component
by Th44;
