The Infintesimal Prolongation Theorem is extended from sequences to nets in κ-saturated nonstandard model. As its application, a main property about the topology of uniform convergence is proved. The proof is much si...The Infintesimal Prolongation Theorem is extended from sequences to nets in κ-saturated nonstandard model. As its application, a main property about the topology of uniform convergence is proved. The proof is much simpler than it was; meanwhile, the nonstandard characteristics of convergence with respect to u.c. topology are given.展开更多
The structure and some properties of ＊τx are discussed in the nonstandard κ-saturated model in this paper. First, a sufficient and necessary condition of a internal set in ＊τx is given. Then, in κ-saturation, so...The structure and some properties of ＊τx are discussed in the nonstandard κ-saturated model in this paper. First, a sufficient and necessary condition of a internal set in ＊τx is given. Then, in κ-saturation, some properties of ＊τx are proved. Finally, the approach theorem is easily obtained.展开更多
Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much ...Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.展开更多
基金Procject supported by the Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province, China
文摘The Infintesimal Prolongation Theorem is extended from sequences to nets in κ-saturated nonstandard model. As its application, a main property about the topology of uniform convergence is proved. The proof is much simpler than it was; meanwhile, the nonstandard characteristics of convergence with respect to u.c. topology are given.
基金Foundation item:the Natural Science Foundation of Shaanxi Province(2007A12)the Basic Research Foundation of Xi'an Arch.&Tech.University(JC0620)the Youth Science Technology of Xi'an Arch.&Tech.University (QN0736)
文摘The structure and some properties of ＊τx are discussed in the nonstandard κ-saturated model in this paper. First, a sufficient and necessary condition of a internal set in ＊τx is given. Then, in κ-saturation, some properties of ＊τx are proved. Finally, the approach theorem is easily obtained.
基金Supported by the Speaial Science Foundation of the Edneational Committee of Shaanxi Province(oojk207).
文摘Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.
