:: deftheorem defines is_point_conv_on SEQFUNC2:def 7 :
for D being non empty set
for Y being RealNormSpace
for H being Functional_Sequence of D, the carrier of Y
for X being set holds
( H is_point_conv_on X iff ( X common_on_dom H & ex f being PartFunc of D, the carrier of Y st
( X = dom f & ( for x being Element of D st x in X holds
for p being Real st p > 0 holds
ex k being Nat st
for n being Nat st n >= k holds
||.(((H . n) /. x) - (f /. x)).|| < p ) ) ) );