STRONGLY UNIFORMLY PARACOMPACT SPACES
In modern Topology, there are the following approaches to the definition strongly uniform paracompactness: strongly uniform -paracompactness [3], strongly uniform paracompactness [6]. In this article, we study a uniform analog of - strongly paracompact spaces. A simple topological lemma that a topological space is - strongly paracompact if and only if each of its finitely additive open covering can be refinement a - star open covering served as the basis for our definition: a uniform space is called is -strongly uniform paracompact if each of its finitely additive open covering can be refinement a - star uniform covering. For a finite cardinal we obtain the definition of strongly paracompactness. The topology of any - strongly uniform paracompact space is -strongly paracompact. If a topological space is - strongly paracompact, then a uniform space with universal uniformity is -strongly uniformly paracompact. The connections with other uniformly properties are studied, for example, compact spaces, strongly uniformly paracompact spaces, -strongly uniformly locally compact spaces. The characteristics of these classes of uniform spaces are given, using Hausdorff compact extensions, Stone-Cheh extensions and uniformly perfect continuous mappings of uniform spaces. It is shown that these are inherited by closed subspaces. It is proved that the product of a compact uniform space on -strongly uniformly paracompact space is -strongly uniformly paracompact, the sum of a - strongly uniformly paracompact space is - strongly uniformly paracompact.