theorem Th76: :: TOPGEN_5:76

for U being Subset of Niemytzki-plane
for x being Real
for r being positive Real st U = (Ball (|[x,r]|,r)) \/ {|[x,0]|} holds
ex f being continuous Function of Niemytzki-plane,I[01] st
( f . |[x,0]| = 0 & ( for a, b being Real holds
( ( |[a,b]| in U ` implies f . |[a,b]| = 1 ) & ( |[a,b]| in U \ {|[x,0]|} implies f . |[a,b]| = (|.(|[x,0]| - |[a,b]|).| ^2) / ((2 * r) * b) ) ) ) )