On the domain invariance of countably condensing vector fields
It is shown that continuous maps of the form \(\text{ id}-F\) are open if they are locally one-to-one and if \(F\) decreases a measure of noncompactness of countable sets by at least a factor \(k<1\). Actually, the injectivity hypothesis is slightly relaxed. Since the first assumption is satisfied for compact maps, the classical results on the domain invariance of injective functions are a special case.
scientific article; zbMATH DE number 2174924