On diffeomorphisms deleting weak compacta in Banach spaces
We prove that if X is an infinite-dimensional Banach space with smooth partitions of unity then X and X∖ K are diffeomorphic for every weakly compact set K ⊂ X.
We prove that if X is an infinite-dimensional Banach space with smooth partitions of unity then X and X∖ K are diffeomorphic for every weakly compact set K ⊂ X.
The class of locally connected and locally homeomorphically homogeneous topological spaces such that every one-to-one continuous mapping of an open subspace into the space is open has been considered. For a foliation F [3] on a Sikorski differential space M with leaves having the above properties it is proved that for some open sets U in M covering the set of all points of M the connected components of U ∩ L̲ in the topology of M coincide with the connected components in the topology of L for L∈...