reserve x, y, z for set,
  T for TopStruct,
  A for SubSpace of T,
  P, Q for Subset of T;
reserve TS for TopSpace;
reserve PS, QS for Subset of TS;

theorem
  for TS being non empty TopSpace holds TS is T_2 & TS is compact
  implies TS is regular
by Th6,Th8;
