
theorem
  for M being non empty MetrSpace, P being non empty Subset of
TopSpaceMetr M, z being Point of M st P is compact holds ex w being Point of M
  st w in P & (dist_max P) . z >= dist (w, z)
proof
  let M be non empty MetrSpace, P be non empty Subset of TopSpaceMetr M, z be
  Point of M;
  assume
A1: P is compact;
  consider w being object such that
A2: w in P by XBOOLE_0:def 1;
  reconsider w as Point of M by A2,TOPMETR:12;
  take w;
  thus w in P by A2;
  thus thesis by A1,A2,Th20;
end;
