L-模糊拓扑中广义Tychonoff定理的新证明

利用赵虎等人介绍的(L, L)-模糊拓扑乘积空间的结构,对L-模糊拓扑中的广义Tychonoff定理给出直接的证明,从而使研究者较容易地理解这一定理.

拓扑空间及其运算

讨论拓扑空间的可积性、遗传性、可和性和局部性质，通过例子说明一些拓扑性质不满足这些运算，并提出几个问题．

一类特殊的拓扑空间——θ-复形

发展了Dikranjan构造若干个Hausdorff非正则的想法,给出了一类特殊拓扑空间——θ-复形的定义,并列举了几个典型例子进行说明.

拓扑空间的计算环境(英文)

讨论了Tychonoff空间的计算环境.主要结论有:Choquet完备的弱domain,其极大点空间也是Choquet完备的;拓扑空间X是Tychonoff空间当且仅当X有一有界完备的弱环境;Tychonoff空间的Hausdorff紧化可以通过其计算环境实现.

A&zeta;x- and Open <i>C_D^*</i>-Filters Process of Compactifications and Any Hausdorff Compactification

By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X?can be obtained from a by the?similar process in Sec.3.

LF拓扑空间的的r-紧性

引入了r-基,r-子基,r-紧等概念,给出了r-紧性的网式刻画,证明了r-紧性是闭遗传,被r-连续的格值Zadeh型函数所保持,Tychonoff乘积定理成立等结果。

Order Environments of Topological Spaces

In this paper it is proved that a space may be realized as the set of the maximal elementsin a continuous poset if and only if it is Tychonoff.

Lω-空间中的ω-Tychonoff分离性

在Lω-空间中,借助于ω-连续的L值Zadeh型函数,给出ω-Tychonoff分离性的定义,并系统研究ω-Tychonoff分离性的特征性质。证明ω-Tychonoff分离性是可遗传的、任意可乘的、ω-弱同胚不变的。