CHARACTERIZATIONS OF SUBIMMERSIONS AND RANK THEOREMS IN BANACH SPACES

Abstract

In this paper, some characterizations of subimmersion are obtained. Our theorems not only unify the classical local immersion theorem, the classical local submersion theorem, the classical local subimmersion theorem and the finite rank theorem but also really generalize them. As applications, we also give some characteristic conditions for the nonlinear Fredholm maps and nonlinear semi-Fredholm maps being subimmersions, which are a generalization and an extension of Berger's rank theorem of nonlinear Fredholm maps in advanced calculus.