CROSS-SECTIONS OF SOLUTION FUNNELS IN BANACH-SPACES

The present paper applies negligibility theory (a part of infinite-dimensional topology) to study the geometry of the failure of Kneser's theorem in infinite-dimensional Banach spaces. In particular, it turns out that arbitrary compact subsets of the infinite-dimensional separable Hilbert space can be represented as cross-sections of solution funnels. For general infinite-dimensional Banach spaces, the existence of initial value problems with exactly two solutions is proved.