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1·We also study the base and subbase in the product space of I-fuzzy topological Spaces.

此外，文中界定了乘积空间中基与子基并研究了乘积空间与因子空间的关系。

2·In the inner product space, the existence theory of best approximation element was obtained and described.

获得了内积空间关于弱闭凸集的最佳逼近元的存在性及其刻划定理。

3·There are many different types of abstract space in mathematics, for examples, vector space, inner product space, etc.

数学上存在各种不同的抽象空间，例如向量空间，内积空间等。

4·In this paper, the vertical concept on the fuzzy inner product space is given and a regular vertical base is introduced.

文章给出了模糊内积空间中垂直的定义，介绍了正规正交基，然后利用它讨论了模糊内积空间的一些性质，并证明了勾股定理。

5·A kind of permutation operators in the direct product space of coherent-states isderived in terms of the coherent-state method.

本文用相干态方法导出了相干态直积空间中的一类置换算符，给出了它们的正规序形式和显式形式，并讨论了置换算符的一些性质。

6·Klinger warns: It's easy to take the policy implication too far and start trying to pick and choose where to settle in the product space.

科林格提醒道：“人们很容易把政策含意理解得过远，开始尝试在产品空间中挑选栖身之地。”但这是一大进步。

7·We also discuss the APOTP of the product map on the finite product space and show that the shift map on infinite product space has the APOT p.

讨论了有限积空间上积映射的APOTP并证明无限积空间上移位映射具有APOTP。

8·A collectively fixed point theorem for a family of set-valued mappings defined on a product space of locally generalized convex uniform Spaces is first proved.

对一族定义在局部广义凸一致空间的乘积空间上的集值映射，给出了一个集族不动点定理。

9·A section theorem, a minimax inequality and a generalized fixed point theorem where the underlying space is a product space of two topological vector Spaces, are given.

给出了两个拓扑向量空间的乘积空间上截口定理，极小极大不等式及一个推广的不动点定理。

10·Based on the minimizing vector theorem of the fuzzy inner product space, the pseudo fuzzy orthogonal vector is defined and the projected theorem of the fuzzy inner product space is testified.

在模糊内积空间的极小化向量定理基础上，给出了向量拟模糊正交定义，并在模糊内积空间中证明了投影定理。