  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 $X,Y$
for which $\Ext(X,Y)$ is Hausdorff and non-zero?). In fact, we show that these
two problems are the same.
