In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and c...In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and closed images of locally separable metric spaces,and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces.展开更多
This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference be...This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference between two elements. The motivation arises from studying random elements talking values in N.B.A. Those topological properties are important assumptions that enable us to avoid possible difficulties when generalising concepts of random variable convergence, the definition of conditional law and others. For each N.B.A., there exists a finite measure space ( E,ℰ,μ ) such that the N.B.A. is isomorphic to ( ℰ ˜ , μ ˜ ) resulting from the factorisation of initial σ-algebra by the ideal of negligible sets. We focus on topological properties ( ℰ ˜ , μ ˜ ) in general setting when μ can be an infinite measure. In case when μ is infinite, we also consider properties of ℰ ˜ fin ⊆ ℰ ˜ consisting of classes of measurable sets having finite measure. The compactness and separability of the N.B.A. are characterised using the newly defined terms of approximability and uniform approximability of the corresponding measure space. Finally, conditions on ( E,ℰ,μ ) are derived for separability and compactness of ℰ ˜ and ℰ ˜ fin .展开更多
Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two ...Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.展开更多
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
基金Supported by the National Natural Science Foundation of China
文摘In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and closed images of locally separable metric spaces,and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces.
文摘This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference between two elements. The motivation arises from studying random elements talking values in N.B.A. Those topological properties are important assumptions that enable us to avoid possible difficulties when generalising concepts of random variable convergence, the definition of conditional law and others. For each N.B.A., there exists a finite measure space ( E,ℰ,μ ) such that the N.B.A. is isomorphic to ( ℰ ˜ , μ ˜ ) resulting from the factorisation of initial σ-algebra by the ideal of negligible sets. We focus on topological properties ( ℰ ˜ , μ ˜ ) in general setting when μ can be an infinite measure. In case when μ is infinite, we also consider properties of ℰ ˜ fin ⊆ ℰ ˜ consisting of classes of measurable sets having finite measure. The compactness and separability of the N.B.A. are characterised using the newly defined terms of approximability and uniform approximability of the corresponding measure space. Finally, conditions on ( E,ℰ,μ ) are derived for separability and compactness of ℰ ˜ and ℰ ˜ fin .
基金Supported by National Natural Science Foundation of China(Grant No.10871016)
文摘Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.
