论文标题:L-拓扑空间的分离性
The Investigation of Some Problems in Ramsey Theory
论文作者 郝俊玲
论文导师 郑崇友,论文学位 硕士,论文专业 基础数学
论文单位 首都师范大学,点击次数 155,论文页数 17页File Size731k
2003-04-01论文网 http://www.lw23.com/lunwen_514424347/ L-拓扑空间;α-完全T2L-拓扑空间;层完全T2L－拓扑空间;T2(1/2)L-拓扑空间;ST2(1/2)L-拓扑空间;强半正则L-拓扑空间
L- Topological space, α-completely T2 L-topological space, Stratified completely T2 L-topological space, T2(1/2) L-topological space, ST2(1/2) L-topological space, Strong semi-regular L-topological space
分离性是拓扑学中重要研究课题之一。本文研究L-拓扑空间的分离性，共分两节。 第一节的内容是：在L-拓扑空间中引入一种层完全T_2分离性，它是一般拓扑中完全T_2分离性的L-好推广。这种层完全T_2分离性具有弱同胚不变性，遗传性，在积运算下保持等性质，且弱诱导的层T_1的层正则L-拓扑空间是层完全T_2的。 第二节的内容是：通过一个例子说明在[13]中定理2.2“设(L~X，ω_ι(T))是由分明拓扑空间(X，T)拓扑生成的L-拓扑空间，则(L~X，ω_ι(T))是T_(2 1/2)空间当且仅当(X，T)是T_(2 1/2)空间。所以T_(2 1/2)空间是L-好的推广”的证明中用到的一个结论是错误的，并给出该定理的一种正确证明。最后，文中给出了强半正则L-拓扑空间的一种等价刻画。
Separation axiom is one of the important studied content in topology.In this paper, separation axioms in L-topological spaces are studied ,there are two sections .In the first section: the concept of stratified completely T2 separation is introduced in L- topological spaces. It is a L-good extention , a invariant of weak homeo-morphisms, and it is hereditary,producible. Furthemore , a weakly induced stratified T1 and stratified regular space is a stratified completely T2 space .The second section: It illustrates that a conclusion ( (P ) [ (P)] ) is wrong which is used by the proof of theorem 2.2 of [13] via a example . It also gives a right proof of this theorem. Finally, this paper gives an equivalent description of strong semi-regular L-topological space. " Theerem 2.2 of [13]: Supposing that (Lx, t( )) is a L-topologcal space that is topologocal generated by crisp topological space (X, T) , then (Lx, t( )) is a T21/2 space if and only if (X, T) is a T21/2 space. So T21/2 space is a L-good extentation
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