Stability constants and the homology of quasi-Banach spaces

摘要

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 isfinite while the approximation constant is infinite?) and by Cabello andCastillo in \emph{The long homology sequence for quasi-Banach spaces, withapplications}, Positivity 8 (2004) 379--394 (do there exist Banach spaces $X,Y$for which $\Ext(X,Y)$ is Hausdorff and non-zero?). In fact, we show that thesetwo problems are the same.