共查询到20条相似文献，搜索用时 15 毫秒
1.
In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable. 相似文献
2.
By using dressing actions of the Gn-1,n-1^1,1-system,the authors study geometric transformations for flat time-like n-submanifolds with flat,non-degenerate normal bundle in anti-de Sitter space H1^2n-1(-1),where Gn-1,n-1^1,1=0（2n-2,2/O(n-1,1)×O(n-1,1). 相似文献
3.
A. V. Arhangel'skii R. Z. Buzyakova 《Proceedings of the American Mathematical Society》1999,127(8):2449-2458
We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.
4.
Udayan B. Darji 《Proceedings of the American Mathematical Society》1996,124(1):129-134
Suppose that is a sequence of differentiable functions defined on [0,1] which converges uniformly to some differentiable function , and converges pointwise to some function . Let . In this paper we characterize such sets under various hypotheses. It follows from one of our characterizations that can be the entire interval [0,1].
5.
给出了某类解析簇上具有非孤立奇点的函数芽f在某种等价关系下的C~0-R_V-V(f)-充分性及它的某些形变平凡性的充分条件.它推广了具有非孤立奇点的函数芽的R-Z-充分性的一个判别准则. 相似文献
6.
In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of $mathsf {CH}$ by adding a real. 相似文献
7.
Peter Nyikos Leszek Piatkiewicz 《Proceedings of the American Mathematical Society》1996,124(1):303-314
In 1975 E. K. van Douwen showed that if is a family of Hausdorff spaces such that all finite subproducts are paracompact, then for each element of the box product the -product is paracompact. He asked whether this result remains true if one considers uncountable families of spaces. In this paper we prove in particular the following result: Let be an infinite cardinal number, and let be a family of compact Hausdorff spaces. Let be a fixed point. Given a family of open subsets of which covers , there exists an open locally finite in refinement of which covers . We also prove a slightly weaker version of this theorem for Hausdorff spaces with ``all finite subproducts are paracompact" property. As a corollary we get an affirmative answer to van Douwen's question.
8.
Roland Sh. Omanadze 《Mathematical Logic Quarterly》2013,59(3):238-246
We study the degree structure of bQ‐reducibility and we prove that for any noncomputable c.e. incomplete bQ‐degree a, there exists a nonspeedable bQ‐degree incomparable with it. The structure $mathcal {D}_{mbox{bs}}$ of the $mbox{bs}$‐degrees is not elementary equivalent neither to the structure of the $mbox{be}$‐degrees nor to the structure of the $mbox{e}$‐degrees. If c.e. degrees a and b form a minimal pair in the c.e. bQ‐degrees, then a and b form a minimal pair in the bQ‐degrees. Also, for every simple set S there is a noncomputable nonspeedable set A which is bQ‐incomparable with S and bQ‐degrees of S and A does not form a minimal pair. 相似文献
9.
In this paper, the irreducible p, q‐representations of the Lie algebras $mathcal {G}(0,1)$ and $mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model. 相似文献
10.
We construct a global solution with $mathcal {C}^{k}$‐estimates for the $bar{partial }$‐equation on q‐convex intersections. 相似文献
11.
Antonio Aizpuru Francisco Javier Garcia-Pacheco 《Proceedings of the American Mathematical Society》2006,134(7):2109-2115
The aim of this paper is to study the set of all -summand vectors of a real Banach space . We provide a characterization of -summand vectors in smooth real Banach spaces and a general decomposition theorem which shows that every real Banach space can be decomposed as an -sum of a Hilbert space and a Banach space without nontrivial -summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces.
12.
Corrado Marastoni 《Mathematische Nachrichten》2013,286(10):992-1006
Given a pair of dual generalized flag manifolds of a semisimple algebraic group, we show that the integral transform between them given by the open orbit in their product is an equivalence. We also describe the links of this problem with the structure of generalized Verma modules, and how the above construction can be applied to the representation theory of real forms of the group. 相似文献
13.
J. Hagler 《Proceedings of the American Mathematical Society》2002,130(11):3313-3324
Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .
14.
In this note, we show that each fragmentable space introduced by Jayne and Rogers in 1985 is of class which was introduced by Kenderov in 1984. Our example shows that a space which is of class may not be a fragmentable space.
15.
It is shown that a separable Banach space can be given an equivalent norm with the following properties: If is relatively weakly compact and , then converges in norm. This yields a characterization of reflexivity once proposed by V.D. Milman. In addition it is shown that some spreading model of a sequence in is 1-equivalent to the unit vector basis of (respectively, ) implies that contains an isomorph of (respectively, ).
16.
在这篇文章中, 我们引入了$Pm$-可分解拓扑群的概念. 令$G$是一个拓扑群, 若对于$G$到一个可度空间$M$上的每一个连续函数$f: Grightarrow M$, 都存在第二可数拓扑群$K$ 以及完备同态映射$pi: Grightarrow K$ 和连续函数$g: Krightarrow M$使得$f=gcircpi$, 那么我们称$G$是$Pm$-可分解拓扑群. 我们证明了一个拓扑群$G$是$Pm$-可分解拓扑群当且仅当$G$是$Pmathbb{R}$-可分解拓扑群. 并且我们证明了: 若$G$是$Pm$-可分解拓扑群, $K$是任一紧拓扑群, 则$Gtimes K$ 是$Pm$-可分解拓扑群. 相似文献
17.
设A是Abel范畴,F是Ext_A~1(-,-):A~(op)×A→A的加法子双函子.首先研究了Ext_(F-)投射生成子与Ext_F-内射余生成子的同调性质,其次引入了W_F-Gorenstein模的概念.特别地,证明了如果重复W_F-Gorenstein模的定义程序将不会产生新的模类.最后,统一并推广了许多参考文献中的结论. 相似文献
18.
19.
E. G. Kwon 《Proceedings of the American Mathematical Society》1996,124(5):1473-1480
If is a holomorphic self-map of the open unit disc and , then the following are equivalent. for all Bloch functions .
where is the hyperbolic derivative of : .
20.
Alexander Shibakov 《Proceedings of the American Mathematical Society》1996,124(8):2599-2607
Using CH we construct a countable sequential topological group whose sequential order is between and giving a consistent negative answer to P. Niykos' question.