关于半同胚空间类的最强和最弱拓扑

Strongest And Weakest Topology in Class of Soni-homemorphic Spaces

本文从半同胚空间类的所有拓扑出发,以集合运算代替拓扑运算,给出直接用这些拓扑描述的最强和最弱拓扑的结构,方法简捷,结果直观。引理设(X,U)是拓扑空间,集S(?)X是半开集,当且仅当S适合条件:若S∩V≠φ,则(?)u(?)S∩V,其中V∈U,u∈u\{φ}。定理半同胚空间类{U_i}_(iel)中有最强拓扑u,即为以族∪U_i生成的拓扑。定理半同胚空间类{U_i}_(iel)中最弱拓扑U_0=∩U_i,只要∩U_i构成U_i的基,Vi∈I。

This essey starts with all topologies of the class of semi--homerphic spac-es, superseding topological opeeration with operation of sets, offers the stru-ctures of the strongest and weakest topology directly described with these to-Pologies. Completely diffrent with the others study, the method of this essay is-not only simple and direct, but it also has a audio--visual result. Lemma let (X, U) be a topological space, then S(?)X is a semiopen set ifand only if S fits the condition, if S∩V≠(?), then(?)u(?)s∩V, where V∈U,u∈u(?){(?)}. Theorem there exists in class {U_i}_(iel) of semi--home--morphic space thestrongest topology U, it is topology generated by the subbase. Theorem the weakest topology exists in class {U_(i)} _(iel) of thesemi--homemorphic spasses on condi--tion that U_0, forms a base of U_i, (?)i∈I.