Stability constants and the homology of quasi-Banach spaces
arXiv:1307.4382
Abstract
We affirmatively solve the main problems posed by Laczkovich and Paulin in \emph{Stability constants in linear spaces}, Constructive Approximation 34 (2011) 89--106 (do there exist cases in which the second Whitney constant is finite while the approximation constant is infinite?) and by Cabello and Castillo in \emph{The long homology sequence for quasi-Banach spaces, with applications}, Positivity 8 (2004) 379--394 (do there exist Banach spaces for which $\Ext(X,Y)$ is Hausdorff and non-zero?). In fact, we show that these two problems are the same.
arXiv commentThis paper is to appear in Israel Journal of Mathematics