:: deftheorem defines equibounded ASCOLI:def 2 :
for S being non empty MetrSpace
for T being RealNormSpace
for F being Subset of (Funcs ( the carrier of S, the carrier of T)) holds
( F is equibounded iff ex K being Real st
for f being Function of the carrier of S, the carrier of T st f in F holds
for x being Element of S holds ||.(f . x).|| <= K );