实数集上有限补拓扑空间的研究

Research on Finite Complementary Topological Space on Real Numbers Set

通过对有限补空间ℝ的子空间、道路和收敛序列等问题的讨论,文章研究有限补空间ℝ的连通性、可数性公理、分离性公理和紧性,同时给出什么样的子集是有限补空间ℝ中的连通子集、道路连通子集、局部道路连通子集和紧致子集.

Based uponthe discussion on the subspace,the path and convergent sequences of finite complementary spaceon real numbers set,this paper has probed into the connectivity,countability axioms,separation axioms and compactness which the finite complementary spaceon real numbers set satisfies,and the paper also shows what kind of subset is the connected subset,path connected subset,local path connected subset and compact subset in the finite complementary spaceon real numbers set.