A note on ANRʼs

It is shown that if for a complete metric space (X,d) there is a constant ε>0 such that the intersection of open balls is nonempty for every finite system x1,…,xn∈X of centers and a corresponding system of radii r1,…,rn>0 such that d(xj,xk)⩽ε and d(xj,xk)