I assume the functions need to be continuous, in which case no such sequence exists. The behavior of a continuous function is determined by its behavior on any dense subset.
can someone help me , i now what does mean the sequence of real number , but i confused what does it mean by sequence of vector space? for example vector space of polynomials ? and n*m matrices ?how would be their sentences of the related sequences? and why the convergent of these sequences depends on the norm that we define for these spaces ?