:: deftheorem Def1 defines Gauge JORDAN8:def 1 :

for C being Subset of (TOP-REAL 2)

for n being natural Number

for b_{3} being Matrix of (TOP-REAL 2) holds

( b_{3} = Gauge (C,n) iff ( len b_{3} = (2 |^ n) + 3 & len b_{3} = width b_{3} & ( for i, j being Nat st [i,j] in Indices b_{3} holds

b_{3} * (i,j) = |[((W-bound C) + ((((E-bound C) - (W-bound C)) / (2 |^ n)) * (i - 2))),((S-bound C) + ((((N-bound C) - (S-bound C)) / (2 |^ n)) * (j - 2)))]| ) ) );

for C being Subset of (TOP-REAL 2)

for n being natural Number

for b

( b

b