In pattern analysis and image management, the information of an objective image can be recovered from a sequence approximate images. In mathematical form of expression it is needed to consider some types of continuity...In pattern analysis and image management, the information of an objective image can be recovered from a sequence approximate images. In mathematical form of expression it is needed to consider some types of continuity. Many researchers defined the limit and the upper limit of a sequence and, using the concepts, characterized continuity in the space consisted of images. In the present paper, the authors give firstly some examples to show that there axe some theoretical shortcomings in those results, then give some corresponding correct results.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
基金The projects supported by NNSF of China(10171043 and 19971048)
文摘In pattern analysis and image management, the information of an objective image can be recovered from a sequence approximate images. In mathematical form of expression it is needed to consider some types of continuity. Many researchers defined the limit and the upper limit of a sequence and, using the concepts, characterized continuity in the space consisted of images. In the present paper, the authors give firstly some examples to show that there axe some theoretical shortcomings in those results, then give some corresponding correct results.
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.
