Structure and homomorphisms of microbundles

Abstract

This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold structure. But for microbundles this problem was not yet investigated. Continuous homomorphisms of microbundles are studied. Topologies on families of homomorphisms of microbundles are investigated. Relations of their structure with microbundles are scrutinized. Necessary and sufficient conditions are studied under which families of homomorphism of microbundles in their turn can be supplied with a microbundle structure.