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open subset
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  开子集
     Let V,U be Banach spaces over the same number field and D(T) be an open subset of V, T:D(T)→U.
     设V,U是同一数域上的Banach空间,而D(T)是V的开子集T:D(T)→U. T.
短句来源
     Let Ω be an open subset of R n and f:Ω→R n be a mapping of Sobolev classes W 1,n loc (Ω, R n).
     设Ω是Rn 上的一个开子集 ,如果Sobolev类映射 f∈W1,nloc(Ω ,Rn)是一拟正则映射 ;
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     In this paper, we define a generalized relative degree for A-proper mappings from a relative open subset of a Banach space into another Banach space and introduce the concepts of generalized P-compact and P1-compact mappings.
     本文定义了从一个Banach空间的相对开子集到另一个Banach空间的A-proper映象的广义相对拓扑度并且引入了广义P-紧和P_1-紧概念。
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     Tepological Spaces in which Every Open Subset Has a Compact Boundary
     每个开子集都有紧边界的拓扑空间
短句来源
     Theorem 2 fi is an open subset of Cn+1, is com-plex hypermonogenic functions, then are all complexhypermonogenic functions.
     定理2令Ω是C~(n+1)的一个开子集,f:Ω→A_(n-1)(C)是复超正则函数,则都是复超正则函数。
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  开集
     If D is compact, then the C-functional calculus : C(D) is automatically continuous, where . For a unital Banach algebra B, BG denotes the set of all elements x of B with the spectrum . If G is a bounded open subset of complex field C, then the Riesz functional calculus βG: H(G)×BG→ B is automatically continuous, where βG(f,a )=f(α);
     研究了泛函演算的自动连续性问题.设A是有单位元的C-代数,ND(A)是A中其谱含于紧集D的所有正规元之集,则泛函演算自动连续.对有单位元的Banach代数B,用BG表示B中其谱含于开集G的元素之集,那么当G有界时,Riesz演算自动连续.作为推论得知与均自动连续.
短句来源
     Let A be a unital complex Banach algebra and D be a nonempty open subset of A .
     设A为一有单位元的复Banach代数,D A为非空开集.
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     CartanThullen proved the three equivalent relations that the open subset in C n is holomorphically convex domain in 1932. Another equivalent realation has been proposed in this paper,so we get a new knowlege for the holomorphic convex domain.
     CartanThulen证明了Cn中的开集是全纯凸的三个等价条件,本文将给出另一个等价条件,从而使我们对全纯凸有更新的认识.
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  “open subset”译为未确定词的双语例句
     Let X be a real Banach space with strictly convex dual space X* and G a bounded ,open subset of X.
     设X是一个实Banach空间,X~*为其对偶空间,G是X的开、有界子集。
短句来源
     Let X be a real Banach space with strictly convex dual space X~* and G a bounded,open subset of X.
     设X是一个实B anach空间,X*为其对偶空间,G是X的开、有界子集.
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     is the nonempty open subset of Ω which satisfies u C Ω, and v(z), , is the normal outward versor to at the point x.
     Ω足够光滑的有界区域,Q=Ω×(0,+∞),∑=(?) Ω×(0,+∞)。
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     We have follow result. Let H be a complex Hilbert space. D an open subset of C,f an analytic map- ping of D into H.if ‖f‖ have Maximum value in D Then f Must be analytic function of an Constant vlue.
     本文主要讨论了 H 空间上的最大模得到在区域 D 上取值于 H 空间的解析函数,若模在 D 上取最大值,则必为常值解析函数.
短句来源
     Let D be an open subset of R 2 ,0∈ D,u=(u 1,u 2),V=V(t,u)∈C 1(R 1×(D-{0}),R 1),V(t+T,u)=V(t), and let V u =grad u V(t,u)= (V/u 1,V/u 2). The paper deals with the existence of small periodic solutions of some second order dynamical systems with singular potentials: u¨+V u(t,u)=0 .
     对于如下奇异动力系统:D是含原点的R2中的区域,u=(u1,u2),V=V(t,u)∈C1(R1×(D-{0},R1),且V(t+T,u)=V(t),Vu=graduV(t,u)=(V/u1,V/u2),本文讨论了具有奇异位势(即limV(t,V)=-∞)的二阶动力系统的小周期解的存在性问题:u¨+Vu(t,u)=0。
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  open subset
Equivalently, ifCn, is the total space for a principalGa-bundle over some open subset ofCn-1 then the bundle is trivial.
      
More precisely, we give an algorithm for computing a nonempty open subset of X with a geometric quotient.
      
In this paper we prove that if f is a holomorphic function in a strictly pseudoconvex region D in Cn, n >amp;gt; 1, with radial limit equal to 1 in modulus at each point of some nonempty open subset S of the boundary of D, then f ≡ const in D.
      
Let Ω be an arbitrary, possibly unbounded, open subset of ?n, and letL be an elliptic operator of the form
      
The universal Teichmüller space T may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc.
      
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Let M be a smooth Hilbert manifold, Ω an open subset of M,f:(?)→TMa tangent vector field.Suppose that{M_n}is a sequnce of finite-dimensionalsubmanifolds of M so that(?)M_n=M.Then from f and {M_n},we canobtain a sequexce {f_n:(?)_n→TM_n}of finite-dimensional vector fields.If forany sequence x_(n_j)∈Ω_(nj)so that ||f_(n_j)(x_(n_j)||→0(n_j→∞),there is a subseq-uence x_(n_(j_k))→x so that f(x)=0,then f is said to be A-proper on(?).Inthis paper a generalized degree for A-proper vector fields is established.

本文中给出了 Hilbert 流形上 A—proper 向量场的定义并建立了这种向量场的广义度.

In the present paper, two theorems concerning structures of metric spaces are given. Theorem 1. Let (X,P) be a metric space, then X=IUF~- where I is the set consisting of all isolated points of X and F is a set of first category. The following definitions are needed for the statement of theorem 2. Definition 1. Let (X,ρ) be a metric space, a ∈X. If there exist positive numbers e and c

In the present paper, two theorems concerning structures of metric spaces are given. Theorem 1. Let (X,P) be a metric space, then X=IUF~- where I is the set consisting of all isolated points of X and F is a set of first category. The following definitions are needed for the statement of theorem 2. Definition 1. Let (X,ρ) be a metric space, a ∈X. If there exist positive numbers e and copen subset of U is ε-discrete, then U is called a σ-opsn set, and points of U are called σ-points. Theorem 2. Let (X,ρ) be a metric space and c a positive number less then 1/3, then X= QUDUNUH, where Q is σ-open, D consists of c-dense points which are not σ-points, N has no interior and can be contained in certain e-discrete open set for each positive number ε and H is nowhere dense:

度量空间中点的分布规律如何是关于度量空间最基本的一个问题.本文引入了c—徟点与ε—球散等概念,并给出了度量空间的结构定理.

In this paper, we define a generalized relative degree for A-proper mappings from a relative open subset of a Banach space into another Banach space and introduce the concepts of generalized P-compact and P1-compact mappings. Next, we show several existence theorems of positive solutions for the equations involving these mappings. Our theorems improve and extend some results.

本文定义了从一个Banach空间的相对开子集到另一个Banach空间的A-proper映象的广义相对拓扑度并且引入了广义P-紧和P_1-紧概念。其次,我们证明了含这些映象的方程的正解存在性定理.我们的定理改进和推广了最近的一些结果.

 
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