
theorem Th53:
  for S being TopStruct ex T being TopExtension of S st
  T is strict & the topology of S is prebasis of T
proof
  let S be TopStruct;
  consider T being strict TopSpace such that
A1: the carrier of T = the carrier of S and
A2: the topology of S is prebasis of T by Lm1;
  the topology of S c= the topology of T by A2,TOPS_2:64;
  then reconsider T as TopExtension of S by A1,Def5;
  take T;
  thus thesis by A2;
end;
