theorem Th53: :: JGRAPH_4:53

for cn being Real
for K1 being non empty Subset of (TOP-REAL 2)
for f being Function of ((TOP-REAL 2) | K1),R^1 st - 1 < cn & ( for p being Point of (TOP-REAL 2) st p in the carrier of ((TOP-REAL 2) | K1) holds
f . p = |.p.| * ((((p `1) / |.p.|) - cn) / (1 + cn)) ) & ( for q being Point of (TOP-REAL 2) st q in the carrier of ((TOP-REAL 2) | K1) holds
( q `2 >= 0 & q <> 0. (TOP-REAL 2) ) ) holds
f is continuous