reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A, B for Subset of X;
reserve D for Subset of X;
reserve Y0 for SubSpace of X;
reserve X0 for SubSpace of X;
reserve X0 for non empty SubSpace of X;
reserve X1,X2 for TopStruct;
reserve X1,X2 for TopSpace;
reserve D1 for Subset of X1,
  D2 for Subset of X2;

theorem Th79:
  D1 = D2 & the TopStruct of X1 = the TopStruct of X2 implies (D1
  is closed implies D2 is closed)
by Th76;
