Let $\operatorname{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric $M$ that vanish at base point. We show every normal functional in $\operatorname{Lip}_0(M)^\ast$ is weak$^*$ continuous, answering question by N. Weaver.
This paper is motivated by certain ideas which arise in the theory of differential games (see [3, 41). We abstract the particular features of differential games which are relevant in the notion of a positional game. Suppose S is a topological space, and g is a continuous real-val
Let $(X,d)$ be a pointed compact metric space with the base point $x_{0}$ and let $\Lip((X,d),x_{0})$ $(\lip((X,d),x_{0}))$ denote the pointed (little) Lipschitz space on $(X,d)$. In this paper, we prove that every weakly compact composition operator $u C_{\varphi}$ on $\Lip((X,d