ABOUT (STRONG) - FINALLY PARACOMPACT AND UNIFORMLY - FINALLY PARACOMPACT SPACES
It is well known that paracompactness play an important role in General Topology. Recently, a theory of compact space type has been intensively developed. In the uniform topology, there are different versions of the uniform paracompactness of uniform spaces. For example, uniform - paracompactness in the sense of M.D. Rice [9], uniform - paracompactness in the sense of A.A. Borubaev [2], uniform - paracompactness in the sense of Z. Frolic [7], uniform - paracompactness in the sense of B.A. Pasynkov [8], uniform -paracompactness in the sense of L.V. Aparina [1]. In this article, we study (strong) - finally paracompact and uniformly - finally paracompact spaces. The connection of (strong) - finally paracompact spaces with other topological properties, for example, compact, locally compact spaces.The connection of (strong) - finally paracompact spaces is studied with other topological properties, for example, compact, locally compact spaces.The characteristics of (strong) - finally paracompact spaces by means of - mappings are established, and, in particular, the theorem of V.I. Ponomarev on finally paracompact spaces follows from this characteristic.The characteristics of uniformly - finally paracompact spaces are given in the spirit of Tamano.It is shown that (strong) - finally paracompactness and uniformly - finally paracompactness is inherited by closed subspaces, it is also shown that the product of a compact uniform space into (strong) - finally paracompact (respectively, uniformly - finally paracompact) space (strong) - finally paracompact (respectively , uniformly - finally paracompact) and the completeness of any uniformly - finally paracompact uniform space.