等连续映射拓扑结构的研究
A study of topological structures on equi-continuous mappings
摘要：
EC（Y，Z）是从拓扑空间Y到一致空间Z的等连续映射，本文给出了EC（Y，Z）的函数空间拓扑.性质，如分裂性，容许性等定义的空间。利用网理论研究EC（Y，Z）上函数空间的可裂性和可容许性。证明了开环境拓扑和点传递环境拓扑分别是可容许的和可分裂的。定义了双拓扑。本文证明了EC（Y，Z）上的拓扑是可容许的（分别为当且仅当它的对偶是这样时，分裂）。
英文摘要：
Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic investigations are carried out to provide characterizations of splittingness and admissibility of function spaces on EC(Y,Z). The open-entourage topology and point-transitive-entourage topology are shown to be admissible and splitting respectively. Dual topologies are defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if and only if its dual is so.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
