:: deftheorem defines is_uniformly_continuous_on NCFCONT2:def 1 :
for X being set
for CNS1, CNS2 being ComplexNormSpace
for f being PartFunc of CNS1,CNS2 holds
( f is_uniformly_continuous_on X iff ( X c= dom f & ( for r being Real st 0 < r holds
ex s being Real st
( 0 < s & ( for x1, x2 being Point of CNS1 st x1 in X & x2 in X & ||.(x1 - x2).|| < s holds
||.((f /. x1) - (f /. x2)).|| < r ) ) ) ) );