  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.
