The Study Of Several Classes Of Compactness In Topological Space By Nonstandard Method

Topology has promoted the progress of analytics greatly. The concept and tech-nology of the topology have been widely applied to many subjects. It is necessary tostudy the propery of compact, which is the key concept in topology.Nonstandard analysis theory has developed rapidly recently. It has been appliedto classical mathematics and phisics theory, especially in unlimited and micro aspect.Nonstandard analysis theory is introduced to Topology in this paper.Firstly, the related theory of nonstandard analysis is described, including thestructure in nonstandard global domain and standard global domain, formal language,and the configuration of nonstandard model with its nature.Secondly, the topology is redefined by monad. The related defination and certifi-cation is proposed.Finally, the nonstandard characterization is provided in compact, locally compact,relatively compact situation. It proves that the nonstandard characterization agreeswell with the definition of nonstandard analysis. The natrue of three compact spacepruduct is obtained by intruducing the conversion principle and internal theorem.Nonstandard analysis can not only makes the definition original standard analysisclear, but also simplifies the certification. It has the same consistency with the normaltopology. Also, it can improve the progress the nonstandard analysis theory in topology.It provides a novel method in the study of Tomology, and has some reference value andpractical significance.