共查询到20条相似文献,搜索用时 93 毫秒
1.
2.
3.
4.
5.
本文讨论了F数的扩张加法和扩张数乘运算的性质;并举反例说明这样的扩张运.算不能使F数全体F*构成线性空间;最后对可列个F数的运算进行了讨论. 相似文献
6.
讨论了拓扑空间上内部运算的性质,并对满足内部运算前三条性质的一类运算,引入一种等价关系,将这些运算进行等价分类,证明了每个等价类中的所有运算导出同一个拓扑,并进一步证明了每个等价类中仅有一个是内部运算且是等价类中的最小元. 相似文献
7.
对点集拓扑学中由导集运算决定拓扑的方法进行了讨论,给出了导集运算的定义,导集运算决定拓扑定理,并讨论了导集运算中条件的相互独立性.进一步完善了点集拓扑学中有关导集概念的内容. 相似文献
8.
10.
11.
J. AlmeidaL. Barreira 《Journal of Mathematical Analysis and Applications》2002,268(2):590-601
For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the classical notion. 相似文献
12.
Neil Epstein 《代数通讯》2015,43(1):325-336
Let R be a commutative ring. It is shown that there is an order isomorphism between a popular class of finite type closure operations on the ideals of R and the poset of semistar operations of finite type. 相似文献
13.
A set A in a metric space is called totally bounded if for each ε>0 the set can be ε-approximated by a finite set. If this can be done, the finite set can always be chosen inside A. If the finite sets are replaced by an arbitrary approximating family of sets, this coincidence may disappear. We present necessary and sufficient conditions for the coincidence assuming only that the family is closed under finite unions. A complete analysis of the structure of totally bounded sets is presented in the case that the approximating family is a bornology, where approximation in either sense amounts to approximation in Hausdorff distance by members of the bornology. 相似文献
14.
文中给出了Fuzy有界型空间的定义,在此基础上,讨论了Fuzy有界型空间的等价定理,最后证明了Q-CIFuzy局部凸空间是有界型的. 相似文献
15.
Many examples are known of natural functors describing the transition from categories of generalized metric spaces to the ``metrizable" objects in some given topological construct . If preserves initial morphisms and if is initially dense in , then we say that is -metrically generated. Our main theorem proves that is -metrically generated if and only if can be isomorphically described as a concretely coreflective subconstruct of a model category with objects sets structured by collections of generalized metrics in and natural morphisms. This theorem allows for a unifying treatment of many well-known and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.
16.
主要讨论k-有界sober空间对遗传、收缩、函数空间和Smyth幂构造的封闭性,证明了k-有界sober空间是饱和遗传的,但不是闭遗传的;对收缩与Smyth幂构造均不具有封闭性.还证明了存在k-有界sober空间X使得函数空间[X→X]赋予点式收敛拓扑不是k-有界sober空间. 相似文献
17.
汉诺塔(Tower of Hanoi)问题源于印度一个古老传说,据此做成了益智游戏,蕴含大量的数学思想与方法.本文采用矩阵描述汉诺塔状态和圆盘移动过程,将圆盘从一个位置移动到另一个位置转化为矩阵的加法,进而构造由若干可能状态矩阵组成的图的邻接矩阵,计算其幂矩阵,由此很方便地求得完成汉诺塔游戏的所有可能的圆盘移动方案,求解过程简单,含义清晰,易于理解和实现. 相似文献
18.
I. A. Pyatyshev 《Mathematical Notes》2007,82(5-6):653-659
In the paper, the problem of preserving the property of approximative compactness under diverse operations is considered. In an arbitrary uniformly convex separable space, we construct an example of two approximatively compact sets whose intersection is not approximatively compact. An example of two linear approximatively compact sets for which the closure of their algebraic sum is not approximatively compact is constructed. In an arbitrary Banach space, we construct two nonlinear approximatively compact sets whose algebraic sum is closed but not approximatively compact. We also prove that any uniformly closed Banach space contains an approximatively compact cavity. 相似文献
19.
吴力荣 《应用数学与计算数学学报》2012,26(2):185-192
Sobolev不等式是联系分析和几何的基础不等式之一,而优化Sobolev体是优化Sobolev范数的临界几何核.首先,证明优化Sobolev体的一些仿射性质.然后,运用Barthe的优化迁移方法研究了凸体的特征函数和多胞形仿射函数的优化Sobolev体. 相似文献
20.
Given a complete and cocomplete symmetric monoidal closed category V and a symmetric monoidal V-category C with cotensors and a strong V-monad T on C, we investigate axioms under which an Ob
C-indexed family of operations of the form
x
:(Tx)
v
(Tx)
w
provides semantics for algebraic operations on the computational -calculus. We recall a definition for which we have elsewhere given adequacy results, and we show that an enrichment of it is equivalent to a range of other possible natural definitions of algebraic operation. In particular, we define the notion of generic effect and show that to give a generic effect is equivalent to giving an algebraic operation. We further show how the usual monadic semantics of the computational -calculus extends uniformly to incorporate generic effects. We outline examples and non-examples and we show that our definition also enriches one for call-by-name languages with effects. 相似文献