The space of real-analytic functions has no basis
Volume 142 / 2000
Studia Mathematica 142 (2000), 187-200
DOI: 10.4064/sm-142-2-187-200
Abstract
Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
