扑空

The interrelationship between several basic categories in fuzzy topology is made clear in terms of co-tower extension of topological constructs. It is shown that for ever completely distributive lattice L,the the category of L-fuzzifying topological spaces is isomorphic to the cotower extension of the category of topological spaces, and it can be embbedded in the category of L-topological spaces as a simultaneously reflective and coreflective subcategory.

用拓扑范畴的co-tower扩张的概念厘清了不分明拓扑中若干基本范畴之间的关系，证明了对任意完全分配格L， L-模糊化拓扑空间范畴同构于拓扑空间范畴的co-tower扩张，并且可作为一同时反射余反射子范畴嵌入L-拓扑空间范畴中。

The aim of this paper is to study the countability on I-fuzzy topological spaces.

本文主要是研究I-fuzzy拓扑空间中的可数性，提出I-fuzzy第一可数性、I-fuzzy第二可数性、I-fuzzy可分性、I-fuzzy Lindelf性等几种可数性的概念，界定了它们的特征性质，给出了它们之间的关系，还在第一可数I-fuzzy拓扑空间中用多值序列收敛对映射连续性进行刻画，更为重要的是得到了I-fuzzy拓扑空间中的I-fuzzy Lindelf定理。

The author introduces background about generation of countability in topology and status about the research and the development of count-ability on lattice-valued topological spaces, and gives the main problems to be soled.

文章由六部分组成：第一部分是前言，作者简单介绍了拓扑空间中可数性的产生背景，格值拓扑空间可数性的研究发展情况，给出本文主要的研究问题。

A number of properties of countable topological space were given systematically, such as its countability, separability, compactness and connectedness, including their proofs on the basis of the nature of topological space, real number space and corresponding theorems.

摘要在可数补拓扑空间的拓扑性质的研究基础上，系统的给出了可数补拓扑空间的可数性，分离性，紧致性，连通性等性质，并给予证明。

The fourth section is the reseach about I-fuzzy separability and I-fuzzy Lindelof property. The author introduces the concepts of I-fuzzy separability and I-fuzzy Lindelof property, and proves that the degree to I-fuzzy second countability in each of I-fuzzy topological spaces must be less than that to I-fuzzy separability and I-fuzzy Lindelof property.

第四部分是关于I-fuzzy可分性和I-fuzzy Lindelf性的研究，作者引入了I-fuzzy拓扑空间中I-fuzzy可分性和I-fuzzy Lindelf性的概念，证明了一个I-fuzzy拓扑空间是第二可数的I-fuzzy拓扑空间的程度一定小于它是可分的I-fuzzy拓扑空间的程度，也一定小于它是Lindelf的I-fuzzy拓扑空间的程度这也是著名的I-fuzzy Lindel

The author uses I-fuzzy quasi-coincident neighborhood system to introduce the concepts of I-fuzzy first countability and I-fuzzy second countability, and proves the degree to second countability in each of I-fuzzy topological space must be less than that to first countability, and gives the equivalent characterations about the continuity of function by convergence of sequences in first countable I-fuzzy topological spaces.

作者利用方进明在[4]中提出的I-fuzzy重域系引入了I-fuzzy拓扑空间的第一可数性和第二可数性的概念，证明了一个I-fuzzy拓扑空间空间是第二可数的I-fuzzy拓扑空间的程度一定小于它是第一可数的I-fuzzy拓扑空间的程度，并且在第一可数的I-fuzzy拓扑空间中对映射的连续性进行了等价刻画。

It is a main task of General Topology to compare different spaces.

一般拓扑学的一个主要任务是不同拓扑空间类的比较，映射直接建立了不同拓扑空间类的联系，是实现该任务的重要工具。

Three counter-examples of topological space are proposed in this study: There are two metric spaces, X and Y, in which and are isometric, whileand are not isometric; Non-metric tight regular space is a counter-example of the separation of topological space; No non-zero continuous linear functionals of the linear topological space is a counter-example of linear topological space.

这里给出三个反例，存在两个度量空间X与Y，使X^2与Y^2等距而X与Y并不等距是拓扑空间中的反例；存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例；不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例。

In this paper, based on local compactness in topological spaces, local N-compactness and connectedness in L—topological spaces, we have studied local paxacompactness in topological spaces, local paxacompactness and δ—connectedness in L—topological spaces.

本文以拓扑空间的局部紧性、L-拓扑空间的局部良紧性以及连通性为基础，研究拓扑空间的局部仿紧性、L-拓扑空间的局部仿紧性以及δ-连通性。

Connectedness and δ—connected component are denned. Some properties and equivalent conditions about δ—connected axe given. It is respectively discussed that δ—connected L—topological spaces are abroader than connected L—topological spaces.

定义了L-拓扑空间的δ-连通性和δ-连通分支的概念，讨论了它们的一些性质，给出δ-连通的一些等价刻画，证明了δ-连通L-拓扑空间是比连通L-拓扑空间更广泛的一类空间。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。