Some Topological Properties of a Functor of Finite Degree

In this paper, the connection between a finally compact, pceudocompact, extremely disconnected, -space and its hyperspace is studied. The action of functors on finally compact, pceudocompact, extremely disconnected and -spaces is investigated. Some topological properties of uniformly space and its hyperspace is studied. It is proved: if the uniform space is uniformly paracompact, then is uniformly paracompact. It is also shown: if the uniform space is uniformly -paracompact, then a uniform space is uniformly -paracompact.