Partition of a unity on infinite-dimensional manifold of the Lipschiz class Lip k

Abstract

In the present paper we prove a criterion of Lip k -paracompactness for infinitedimensional manifold M modeled in nonnormable topological vector Frechet space F. We establish that a manifold is Lip k -paracompact if and only if the model space F is paracompact and Lip k -normal. We prove a sufficient condition for existence of Lip k -partition of a unity on a manifold of class Lip k .