On the Domain Invariance Theorem for Accretive Mappings
Rainald Schöneberg · Journal of the London Mathematical Society · 1981
Let E be a Banach space. If D is a subset of E and R a mapping of D into E, then R is said to be accretive if and only if ∥x − y∥ ⩽ ∥(x − y) + t(R(x) − R(y))∥ for all x, y ε D and all t ⩾ 0. Using only this defining property of accretive mappings, we give a straightforward and elementary proof of the important fact that T(U) is open, if U is an open subset of E and T : U → E is continuous, locally closed, locally one to-one and locally accretive.