Connectedness of the efficient point sets in quasiconcave vector maximization (Q1821037)

Let \(X\subseteq R^ n\) be a set of alternatives, f a vector function from X into \(R^ m\) and C a convex closed cone in \(R^ m\). Denote E(X,f) (resp. WE(X,f)) the set of efficient (resp. weakly efficient) alternatives with respect to C. It is established that WE(X,f) is closed connected if f is C-continuous, C-quasiconcave; and E(X,f) is closed connected if f is C-continuous, strictly C-quasiconcave. Under some more conditions E(X,f) is a retract of X, hence contractible when X is convex closed.