Stability constants and the homology of quasi-Banach spaces

摘要

We affirmatively solve the main problems posed by Laczkovich and Paulin in 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 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 nonzero?). In fact, we show that these two problems are the same.