In this paper we establish an equivalence between weakly holomorphic and holomorphic extension for Frechet-valued functions defined on compact subsets in a Prechet space concerning with the linear topological invariant (LBoo) introduced by Vogt [14]. Next, using the linear topological invariant (LBoo) we extend a recent
result of Arendt - Nikolski [1] for Frechet-valued functions on open subsets in Schwartz - Frechet spaces.