1) mesocompact
中紧
1.
Closed Inverse Images of Countable Base-mesocompact Spaces;
基-可数中紧空间的闭逆象
2.
In this paper, We prove that (1) a Tychonoff Space X is mesocompact if and only if every binary open cover of X×βX has a Compact - finite refinement by open rectangles, (2) A regular Space X is mesocompact if and only if every binary open cover of X× 2L(X) has a compact-finite refinement by open rectangles.
本文证明:(1)全正则空间X是中紧的当且仅当X×βX的任何二元开覆盖都有紧有限的开矩形加细,(2)正则空间X是中紧的当且仅当X×2~(L(x))的任何二元覆盖都有紧有限的开矩形加细。
2) concentration compactness
集中紧
1.
This paper discusses the existence of a degenerate nonlinear elliptic equation in unbounded domains by virtue of the concentration compactness principle,the results proving that the equation has no nontrivial solutions in some conditions according to a Pohozear type identity.
利用集中紧原理讨论退化非线性椭圆方程在无界域解的存在性。
4) mesocompactness
中紧性
1.
Topological Game Mesowmpactness and Submesocompactness of Product Spaces;
拓扑博弈与积空间的中紧性及次中紧性
2.
By giving a compact type θ-open covers sequence for the regular submesocompact C-scattered space,we prove two theorems on mesocompactness and submesocompactness of product spaces of which one factor is C-scattered space.
通过给出正则次中紧C-scattered空间的一个紧式θ-开覆盖序列,证明了带C-scattered空间因子的积空间的中紧性和次中紧性的两个定理。
3.
In this paper mesocompactness is characterized in term of well-monotonecover, interior-preserving cover,suborthocompact and cushioned refinement,which improves the results of Guoshi Gao and Lisheng Wu.
本文利用良序单调复盖、内部保持复盖、次ｏｒｔｈｏ－紧及垫状加细等刻画了中紧性。
5) submesocompactness
次中紧性
1.
By giving a compact type θ-open covers sequence for the regular submesocompact C-scattered space,we prove two theorems on mesocompactness and submesocompactness of product spaces of which one factor is C-scattered space.
通过给出正则次中紧C-scattered空间的一个紧式θ-开覆盖序列,证明了带C-scattered空间因子的积空间的中紧性和次中紧性的两个定理。
2.
In this paper,we use topological game as a tool,by establishing a filter property for mesocompactness,to prove several important results on the mesocompactness and submesocompactness of the product spaces of which one factor is satisfied with some game conditions Similar results are obtained for the product spaces of which one factar is a C-scat-tered space.
利用博奕这一工具，通过对次中紧性建立滤子性质，证明了带博奕因子的积空间的中紧性和次中紧性的几个重要结果。
6) submesocompact space
次中紧
1.
The image if a submesocompact space under a closed and compact-covering mapping is submesocompact.
本文得到如下主要结果:一个空间是次中紧的当且仅当它的每个定向开覆盖有σ-闭包保持闭加细使得它被一切紧子集组成的族所加细;次中紧空间在闭的紧覆盖映射下的象是次中紧的;一个空间是可度量的当且仅当它是次中紧的Moore空间。
补充资料：胎紧浸入和套紧浸入
胎紧浸入和套紧浸入
tight and taut immersions
矍数) 图3 犷鳖{ 图4 称空间A CB的嵌人在Z:同调中为单射的(in-Jeetive)，如果对于i)0，诱导同态万.(注，22)~H.(B，22)是单的.令HC=R“是R“中带有超平面边界aH的半空间.例如， H=H:(t)={x“R“:z’(x)簇r}.如果f是一个胎紧浸人，h:是一个非退化的高度函数，那么由Morse理论得到f一’(万:(r))C=M在22同调中是单的.于是由连续性，对任一半空间H这种单性都成立.对于闭流形的光滑浸人，这种半空间性质等价于胎紧性.然而，这种半空间定义也能应用于更大范围的从流形和其他紧拓扑空间到RN中的连续浸人或甚至是映射中去.一个例子是胎紧的“瑞士干酪”，它是一个带边的嵌人曲面，见图5.一个到R中的胎紧映射也称为一个完满函数(详rfect丘inction).公 图5今 图6 对于曲线和闭曲面，半空间性质可导出对任一半空间H，f一’(H)是连通的.它等价于R功ehoff两片性质(R朔chofft场。一pieee pro详rty)，即R“中的任一超平面日H将M至多分割成两个连通的片，见图3和图4中的胎紧曲面和图2中的非胎紧曲线. 半空间定义将胎紧性置于经典几何学和凸性理论之中.由于胎紧性在RN中的任意将凸包才(f(M))映到RN内的射影变换下是不变的，因此胎紧性是一个射影性质(见射影几何学(projeetive罗。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条