reserve Y for TopStruct;

theorem
  for Y being non empty TopStruct, y being Point of Y holds Sspace(y) is
  proper iff {y} is proper
proof
  let Y be non empty TopStruct, y be Point of Y;
  hereby
    reconsider A = the carrier of Sspace(y) as Subset of Y by Lm1;
    assume
A1: Sspace(y) is proper;
    A = {y} by Def2;
    hence {y} is proper by A1;
  end;
  thus thesis by Def2;
end;
