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We prove the following result which extends in a somewhat "linear" sense a theorem by Kierst and Szpilrajn and which holds on many "natural" spaces of holomorphic functions in the open unit disk D: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in D whose domain of holomorphy is D except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space ofdoi:10.4064/sm166-1-4 fatcat:cwqad4hgkzdyxeajkrea2y7rwi