On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

Abstract

Abstract. We show that the solution to the orthogonal additivity problem in real inner product spaces depends continuously on the given function and provide an application of this fact.

On Orthogonally Additive Functions With Big Graphs

“…We shall show more: if a ∈ Hom(R, V ) and U ⊂ Hom(E, V ) is open and non-empty, then {a} × U intersects set (2). To this end we may assume that…”