Topological and algebraic genericity and spaceability for an extended chain of sequence spaces

Given a pair of topological vector spaces $$X,\; Y$$ where X is proper linear subspace Y it examined whether $$Y\setminus X$$ residual in (topological genericity), contains dense except 0 (algebraic genericity) and closed infinite dimensional (spaceability). In the present paper are either sequence or analytic functions on unit disc regarded as via identification function with its Taylor coefficients. For under consideration we give an affirmative answer to each these questions providing general proofs which extend previous results.