reserve Y for TopStruct;
reserve X for non empty TopSpace;

theorem Th28:
  for A0 being non empty Subset of X st A0 is discrete ex X0 being
  discrete strict non empty SubSpace of X st A0 = the carrier of X0
proof
  let A0 be non empty Subset of X;
  consider X0 being strict non empty SubSpace of X such that
A1: A0 = the carrier of X0 by TSEP_1:10;
  assume A0 is discrete;
  then reconsider X0 as discrete strict non empty SubSpace of X by A1,Th20;
  take X0;
  thus thesis by A1;
end;
