商空间映射的连续性及同胚性的讨论

Discussion on the continuity and homeomorphism of quotient space mapping

商空间是构建新拓扑空间的重要方法,对其性质的深入研究具有重要的意义.通过对商映射定义合理性的证明,以及商空间之间映射的连续性和同胚性的证明与讨论,得出了关于商空间映射性质的重要结论,为商空间映射的推广应用提供了严谨的理论依据.

Quotient space is the important method to build the new topological space, studying deeply its quality has important significance. By proving the rationality of quotient mapping＇s definition, and proving and discussing the continuity and homeomorphism of quotient space mapping, gets the quality of quotient space mapping, provides the precise theoretical foundation for popularization and application of quotient space mapping.