This paper proves the following results: let X be a continuum, let k, m ∈ N, and let B ∈ C m (X), consider the continuous surjection f k : C k (X) → C k (X). We define the mapping B : C k (X) → C k+m (X): by B (A)...This paper proves the following results: let X be a continuum, let k, m ∈ N, and let B ∈ C m (X), consider the continuous surjection f k : C k (X) → C k (X). We define the mapping B : C k (X) → C k+m (X): by B (A) = f k (A) B. Then following assertions are equivalent: (1) The hyperspace C k (X) is g-contractible; (2) For each m ∈ N and for each B ∈ C m (X) the mapping B is a W -deformation in C k+m (X); (3) For each m ∈ N there exists B ∈ C m (X) such that the mapping B is a W -deformation in C k+m (X); (4) There exists m ∈ N such that for each B ∈ C m (X) the mapping B is a W -deformation in C k+m (X); (5) There exist m ∈ N and B ∈ C m (X) such that the mapping B is a W -deformation in C k+m (X).展开更多
For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In ...For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.展开更多
Agent-oriented approach is increasingly showing its magic power in a diversity of fields, specifically, ubiquitous computing and smart environment. Meanwhile, it is considered the next creative issue is to interconnec...Agent-oriented approach is increasingly showing its magic power in a diversity of fields, specifically, ubiquitous computing and smart environment. Meanwhile, it is considered the next creative issue is to interconnect and integrate isolated smart spaces in real world together into a higher level space known as a hyperspace. In this paper, an agent-oriented architecture, which involves the techniques of mobile agents, middleware, and embedded artificial intelligence, is proposed. Detailed implementations describe our efforts on the design of terminal device, user interface, agents, and AI展开更多
Let be a metric continuum. Let , is said to make a hole in , if is not unico-herent. In this paper, we characterize elements such that makes a hole in , where is either a smooth fan or an Elsa continuum.
基金Supported by the Department of Education Sichuan Province Foundation for Science Research(2006C041)Supported by the Anhui Provincial Foundation for Young Talents in College(2010SQRL158)
文摘This paper proves the following results: let X be a continuum, let k, m ∈ N, and let B ∈ C m (X), consider the continuous surjection f k : C k (X) → C k (X). We define the mapping B : C k (X) → C k+m (X): by B (A) = f k (A) B. Then following assertions are equivalent: (1) The hyperspace C k (X) is g-contractible; (2) For each m ∈ N and for each B ∈ C m (X) the mapping B is a W -deformation in C k+m (X); (3) For each m ∈ N there exists B ∈ C m (X) such that the mapping B is a W -deformation in C k+m (X); (4) There exists m ∈ N such that for each B ∈ C m (X) the mapping B is a W -deformation in C k+m (X); (5) There exist m ∈ N and B ∈ C m (X) such that the mapping B is a W -deformation in C k+m (X).
文摘For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.
文摘Agent-oriented approach is increasingly showing its magic power in a diversity of fields, specifically, ubiquitous computing and smart environment. Meanwhile, it is considered the next creative issue is to interconnect and integrate isolated smart spaces in real world together into a higher level space known as a hyperspace. In this paper, an agent-oriented architecture, which involves the techniques of mobile agents, middleware, and embedded artificial intelligence, is proposed. Detailed implementations describe our efforts on the design of terminal device, user interface, agents, and AI
文摘Let be a metric continuum. Let , is said to make a hole in , if is not unico-herent. In this paper, we characterize elements such that makes a hole in , where is either a smooth fan or an Elsa continuum.
