A Study Of Suitable Sets For Strongly Topological Gyrogroups

A strongly topological gyrogroup is a special class of topological gyrogroups.At present,there is still have many problems worth to further study for strongly topological gyrogroups.This thesis mainly focuses on the study of suitable sets of(strongly)topological gyrogroups and left(right)strongly topological gyrogroups.In Chapter 1,we introduce the background source and the rsearch status at home and abroad about topological gyrogroups;In addition,we also introduce the define of topological gyrogroups?strongly topological gyrogroups?suitable sets and so on.In Chapter 2,we mainly study the suitable sets of(strongly)topological gyrogroups,we discuss suitable sets of topological gyrogroups and countable topological gyrogroups,we show that each countable Hausdorff topological gyrogroup has a suitable set and each separable metrizable strongly topological gyrogroup has a suitable set.In Chapter 3,we discuss the basic properties of the left(right)topological gyrogroups and suitable sets of the left(right)strongly topological gyrogroups,we show that every countable Hausdorff left(right)strongly topological gyrogroup is generated by a closed discrete subset.In this paper,some results of suitable sets in topological groups are extended to strongly topological gyrogroups,which enrich the content of topological algebra and contribute to the theory research of topological gyrogroups.