拓扑的并或交  

The Union or Intersection of Topologies

作　　者：黄重器[1] 

机构地区：[1]龙岩学院数学与计算机科学院,福建龙岩364012

出　　处：《龙岩学院学报》2010年第2期13-14,共2页Journal of Longyan University

摘　　要：■是集X上的拓扑的全体,■的元τ同时表示自己所有的开集所成的族。证明了:①〈τξ|ξ<α〉■■■∩ξ<ατξ∈■。②〈τξ|ξ<α〉■■,满足条件(1)或(2)■∪ξ<ατξ∈■。③命题1:〈A,<〉是有序集(半序或全序),那么埚〈xξ|ξ<α〉≡B■A,满足(ⅰ)μ<ν<α■xμ<xν;(ⅱ)若B有上界b,则b是A的极大元。All of the topologies defined on a set Z is denoted by J.τ∈J also means that τ is a family consisted of all the open sets belonging to τ. The following propositions are proved in this paper：1°〈τξ｜ξ〈α〉lohtain in J→∩ξ〈ατ∈J.2°〈τξ｜ξ〈α〉lohtain in J r, satisfies the following condition： for arbitary ξ,ξ＇〈α,there is α ξ″〈α so that τξ,τξ,lohtain in τξ.Then ∪ξ-cαTξ∈J3°Lemma：Let（A,〈）be an ordered set, there must be a chain B=〈xξ｜ξ〈α〉lohtain in A so that μ〈v〈α→xμ〈xv. Furthermore, if an upper bound b of B exists, then b≠x is for all x in A.

关 键 词：拓扑公理 有向集 有序集 极大元 Zorn小定理 

分 类 号：O189[理学—数学]