Linear Kierst–Szpilrajn theorems

L. Bernal-González
2005 Studia Mathematica  
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 of
more » ... full space of holomorphic functions. 2000 Mathematics Subject Classification: Primary 30B30; Secondary 30B10, 30D40, 30H05.
doi:10.4064/sm166-1-4 fatcat:cwqad4hgkzdyxeajkrea2y7rwi