Let C(X,Y) be the space of continuous functions from a metric space ( X,d ) to a metric space ( Y, e ). C(X, Y) can be thought as subset of the hyperspace CL(X×Y ) of closed and nonempty subsets of X×Y by identifying each element of C(X,Y) with its graph. We ...
Point-set topology grew out ofCantor's studies of sets of real numbers. As such, its central aim is to provide an appropriate context for generalizing such properties of the real numbers as theBolzano- Weierstrassproperty(波尔查诺-维尔斯特拉斯性质,也叫聚点定理)and theHeine-Borel property(海涅...
作者: JJ Fox,AA Maciejewski 摘要: ABSTRACT 关键词: kinematics manipulators path planning real-time systems topology SCARA manipulators collision-free paths configuration space connectivity kinematics DOI: 10.1109/IROS.1994.407361 被引量: 3 年份: 1994 收藏...
A similar argument confirms that any metric space, in which open sets are induced by a distance function, is a Hausdorff space. However, there are many examples of non-Hausdorff topological spaces, the simplest of which is the trivial topological space consisting of a set X with at least ...
1.1 Topological space 1.2 Neighborhoods and closed sets 1.3 Compactness and connectedness 1.4 Homeomorphisms, homotopy and topological invariants Preface I have started compiling some basic notes on the books and materials I am currently reading that are relevant to my research. The first set of notes...
When a shell is closed it divides all of space into two regions, inside and out. In SMLib a shell is only connected to its inner region and does not pay attention to outer regions. All of the shells of one region, including the outer shell and all the inner shells, treat that region...
Closed and open mappings are one such mappings which are studied for different types of closed sets by vario... RS Wali,PS Mandalageri 被引量: 2发表: 2015年 The ωδ-connectedness in an Lω-space Some new notions on an Lω-space, such as ωδ-closed set, ωδ-open set, ωδ-...
These coefficients are simple functions of the elements of H, and they provide a smooth parametrization of the eigenvalue spectra19. If we take H to be traceless (see “Methods”), then pH has N − 1 coefficients. As these are complex, the space they span (which we denote as LN...
Necessary and sufficient conditions are given so that the space $C(X,E)$ of all continuous functions from a zero-dimensional topological space $X$ to a non-archimedean locally convex space $E$, equipped with the topology of uniform convergence on the compact subsets of $X$, to be polarly...
摘要: This paper presents some properties of singular functionals on Orlicz spaces, from which, criteria for weak convergence and weak compactness in such spaces are obtained.关键词: On weak topology of Orlicz spaces, Artículo 被引量: 4