reserve GX,GY for non empty TopSpace,
  x,y for Point of GX,
  r,s for Real;
reserve Q,P1,P2 for Subset of TOP-REAL 2;
reserve P for Subset of TOP-REAL 2;
reserve w1,w2 for Point of TOP-REAL 2;
reserve pa,pb for Point of TOP-REAL 2,
  s1,t1,s2,t2,s,t,s3,t3,s4,t4,s5,t5,s6,t6, l,sa,sd,ta,td for Real;
reserve s1a,t1a,s2a,t2a,s3a,t3a,sb,tb,sc,tc for Real;

theorem Th26:
  for s1,t1,s2,t2,P st P = { pq where pq is Point of TOP-REAL 2:
  not (s1<=pq`1 & pq`1<=s2 & t1<=pq`2 & pq`2<=t2)} holds P is connected
proof
  let s1,t1,s2,t2,P;
  assume P= { pq where pq is Point of TOP-REAL 2:
  not (s1<=pq`1 & pq`1<=s2 & t1<=pq`2 & pq`2<=t2)};
  then P = {|[sb,tb]| : not (s1<=sb & sb<=s2 & t1<=tb & tb<=t2)} by Th22;
  hence thesis by Th13;
end;
