theorem Th102:
  the carrier of (X modified_with_respect_to X0) = the carrier of
  X & for A being Subset of X st A = the carrier of X0 holds the topology of (X
  modified_with_respect_to X0) = A-extension_of_the_topology_of X
proof
  set Y = X modified_with_respect_to X0;
  reconsider A = the carrier of X0 as Subset of X by TSEP_1:1;
A1: Y = X modified_with_respect_to A by Def10;
  hence the carrier of (X modified_with_respect_to X0) = the carrier of X;
  thus thesis by A1;
end;
