NORMALITY AND COVERING PROFERITIES OF TOPOLOGICAL PROCUCT SPACES

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This study is mainly classified by the following six parts :[1] Characterizations of covering properties in terms of products :We prove some characterizations of metacompactness and submetacompactness in terms of products, and give a complete solution of a problem raised in 1992.[2] Covering properties of products of ordinals :We prove that most covering properties are equivalent in the products of ordinals, and that only subparacompactness is unexpectedly an exception there.[3] Normality of products with a generalized metric factor :Making use of regular nets, we introduced a new concept of generalized metric spaces, and prove the equivalence of normality and countable paracompactness in products with such a generalized metric factor.[4] Metrization theorems in terms of regular k-networks :We prove a natural metrization theorem in terms of regular k-networks. This gives a solution of a problem raised by Nagata.[5] Problems for k-networks and function spaces :M.Sakai has respectively answered two problems for k-networks raised by Lin and Tanaka, and he has also solved a problem for function spaces raised by Bella.[6] Shadowing properties on compact metric spaces :K.Sakai have given a partial answer to the problem of whether shadowing property and Lipschitz shadowing property are equivalent on compact metric spaces.