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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Linear Kierst–Szpilrajn theorems

### Tom 166 / 2005

Studia Mathematica 166 (2005), 55-69 MSC: Primary 30B30; Secondary 30B10, 30D40, 30H05. DOI: 10.4064/sm166-1-4

#### Streszczenie

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 ${\mathbb D}$: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in ${\mathbb D}$ whose domain of holomorphy is ${\mathbb D}$ 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 holomorphic functions.

#### Autorzy

• L. Bernal-GonzálezDepartamento de Análisis Matemático