查询词典 spaces

The proof is given that the category of linear fuzzy neighborhood spaces in the sense of Katsaras is isomorphic to that of co-towers of topological vector spaces and the intersection of the category of linear fuzzy neighborhood spaces with the category of type fuzzy topological vector spaces is the extract category of induced fuzzy topological vector spaces.

证明了Katsaras的线性fuzzy邻域空间范畴与分明线性拓扑空间的余塔空间范畴同构，而Katsaras的线性fuzzy邻域空间范畴与型fuzzy拓扑线性空间范畴的交集恰为诱导的fuzzy拓扑线性空间范畴。

"Two- and three-dimensional Euclidean spaces are metric spaces, as are inner product spaces, vector spaces, and certain topological spaces."

二维和三维的欧几里德空间是度量空间。另外，内乘空间、向量空间以及某些拓扑空间等也都是度量空间

In the first part, the concepts of the completely normal spaces and strong completely normal spaces in L-topological spaces are defined, which are the generalization of the completely normal spaces in general topological spaces. They are some good properties such as hereditary, weakly homeomorphism invariant properties, good L-extension, but they arent producible in general.

第一部分的主要内容如下：第一部分这一部分是将一般拓扑学的完全正规分离性的概念推广到了L-拓扑空间，给出了L-拓扑空间的完全正规分离性和强完全正规分离性的定义并讨论了它们的若干性质，比如，它们都是可遗传的，弱同胚不变的，"Lowen意义下好的推广"等。

In chapter 2, we prove that sn—first countable spaces are preserved by the finite subsequence-covering mappings.By this result, we prove that the finite subsequence-covering, quotient mappings preserve g—metrizable spaces, also prove that the finite subsequence-covering, closed mappings preserve sn—metrizable spaces, g-metrizable spaces, metrizable spaces, point-countable bases.

在第二章中，我们主要证明了有限子序列覆盖映射保持sn-第一可数空间，作为它的应用，又证明了有限子序列覆盖、商映射保持g-第一可数空间，也证明了有限子序列覆盖闭映射保持sn-度量空间，g-度量空间，度量空间，点可数基。

Chapter 3 Some properties in Cesaro-Orlicz sequence spaces: In this chapter, the dual spaces of the Cesaro-Orlicz sequence spaces and the criteria for the extreme point are studied and the sufficient and necessary condition of which the spaces has theλ- property and the uniformλ- property is given by the above results.

第三章Cesaro-Orlicz序列空间中的一些基本性质：本章我们主要讨论了Cesaro-Orlicz序列空间的对偶空间，同时给出此空间中端点的判据，然后由此端点的判据我们证明了Cesaro-Orlicz序列空间具有λ-性质，最后我们得到了此空间中一致λ-性质的等价条件。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

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。

And also,the Holder"s, Minkowski"s,Young-type inequalities and four interpolation theorems,which are hold on the Lebesgue spaces,are established on the homogeneous Morrey-Herz spaces MK_~ and the weak homogeneous Morrey-Herz spaces WMK_~.These results on the cor-responding homogeneous Herz space K_q~and the weak homogeneous Herz spaces WK_q~are also new.

同时把Lebesgue空间上成立的Holder、Minkowski、Young不等式以及四个插值定理推广到了齐次Morrey-Herz空间及弱Morrey-Herz空间WMK_~上，而这些结果在相应的齐次Herz空间K_q~和弱齐次Herz空间WK_q~上也是新的。

In 1936, J.Clarkson first introduced the concept of uniformly convex Banach spaces ,initiated from geometric structure of the unit sphere of Banach spaces to research the properties of Banach spaces, began to research convex theory of Banach spaces. The same year, J.

Clarkson首先引入了一致凸Banach空间的概念，开创了从Banach空间单位球的几何结构出发来研究Banach空间性质的方法，开始了Banach空间凸性理论的研究。

It's really the natural setting for algebraic topology because the traditional algebraic invariants (fundamental group, homolog group,etc.) arc isomorphic not only for homeomorphic spaces but for spaces of the same homotopy type. Homtopy epimorphisms and monomorphisms are special morphisms in the category of topological spaces and the initial research of them may be traceable to S.T.

同伦论的本质是利用比同胚关系更广泛的等价关系—同伦关系来对拓扑空间进行研究，这也是代数拓扑研究中一种自然的考虑，因为传统的代数不变量不仅在同胚的空间之间保持同构，而且在具有相同伦型的空间之间也保持同构。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。