Lineability of the set of holomorphic mappings with dense range
Volume 210 / 2012
Studia Mathematica 210 (2012), 177-188
MSC: Primary 46G20; Secondary 46E50.
DOI: 10.4064/sm210-2-5
Abstract
Let $U$ be an open subset of a separable Banach space. Let $\mathcal{F}$ be the collection of all holomorphic mappings $f$ from the open unit disc $\mathbb{D}\subset \mathbb{C}$ into $U$ such that $f( \mathbb{D}) $ is dense in $U$. We prove the lineability and density of $\mathcal{F}$ in appropriate spaces for different choices of $U$.
