
theorem Th18:
  for X being non empty TopSpace for S being Scott complete
  TopLattice holds oContMaps(X, S) = ContMaps(X, S)
proof
  let X be non empty TopSpace;
  let S be Scott complete TopLattice;
A1: Omega S = the TopRelStr of S & the TopStruct of X = the TopStruct of X
  by WAYBEL25:15;
  thus oContMaps(X, S) = ContMaps(X, Omega S) by WAYBEL26:def 1
    .= ContMaps(X, S) by A1,Th10;
end;
