摘要
Abstract
In this paper, we introduce the concepts of interior operator, neighborhood system operator, base for the neighbor- hood system operator and correspondent axioms from the angle of mapping, then induct topologies and topological spaces. By them , we prove the equivalence between the three conditions of topology and axiom of closed set , axiom of interior , axiom of neigh- bourhood system , axiom of base for the neighborhood system ,and give opposite examples to show the necessities of the conditions in axioms. We also discuss some properties of derived set.关键词
拓扑/拓扑空间/闭集/内部/邻域系/邻域基/导集Key words
Topelogy/topological space/closed set/interior/neighbourhcod system/base for the neighborhood system/de- rived set分类
数理科学
