reserve i,j,k for Nat,
  r,s,r1,r2,s1,s2,sb,tb for Real,
  x for set,
  GX for non empty TopSpace;
reserve GZ for non empty TopSpace;
reserve f for non constant standard special_circular_sequence,
  G for non empty-yielding Matrix of TOP-REAL 2;
reserve G for non empty-yielding X_equal-in-line Y_equal-in-column Matrix of
  TOP-REAL 2;

theorem Th33:
  for G being Matrix of TOP-REAL 2 holds cell(G,i,j) is closed
proof
  let G be Matrix of TOP-REAL 2;
A1: v_strip(G,i) is closed by Th17;
  cell(G,i,j)=h_strip(G,j) /\ v_strip(G,i) & h_strip(G,j) is closed by Th16,
GOBOARD5:def 3;
  hence thesis by A1,TOPS_1:8;
end;
