tailieunhanh - Báo cáo " On the matheron theorem for topological spaces"

In this paper we study the extending of the Matheron theorem for general topological spaces. We also show some examples about the spaces F such that the miss-and-hit topology on those spaces are unseparated or non-Hausdorff. 1. Introduction The Choquet theorem (see [1, 2]) plays very importance role in theory of random sets. The proof of this theorem is based on the Matheron theorem and especially, the locally compact property of the space F , where F is a space of all close subsets of a given space E and F is equipped with the miss-and-hit topology (see [1]). . | VNU Journal of Science Mathematics - Physics 23 2007 194-200 On the matheron theorem for topological spaces Dau The Cap1 Bui Dinh Thang2 1 Hochiminh city University of Pedagogy 280 An Duong Vuong Dist 5 Hochiminh city Vietnam Saigon University 273 An Duong Vuong Dist 5 Hochiminh city Vietnam Received 15 September 2007 received in revised form 1 November 2007 Abstract. In this paper we study the extending of the Matheron theorem for general topological spaces. We also show some examples about the spaces F such that the miss-and-hit topology on those spaces are unseparated or non-Hausdorff. 1. Introduction The Choquet theorem see 1 2 plays very importance role in theory of random sets. The proof of this theorem is based on the Matheron theorem and especially the locally compact property of the space F where F is a space of all close subsets of a given space E and F is equipped with the miss-and-hit topology see 1 . The Matheron theorem is stated as follows. Theorem. Let E be a complete separable and locally compact metric space. Then the miss-and-hit topology on F space of all closed subsets of E is compact separable and Hausdorff Note that the natural domain of the probability theory is a Polish space which is in general not locally compact. So in 3 the authors extended the Matheron theorem for general metric space. They showed that if E is a separable metric space then the miss-and-hit topology on space F is separable and compact. And if E has a non-locally compact point then the miss-and-hit topology on space F is not Hausdorff. Now we extend the Matheron theorem for general topological space. Let E be a topological space. Denote F K and G the families of all close compact and open subsets of E respectively. For every A c E we denote Fa F F eF F n A 0 FA F F eF F n A 0 . For every K E K and a finite family of sets G1 . Gn eg n E N we put FK G. F K n F. n Fc . Then F- . Gn K EK Gi . Gn eg n E N is a base of topology on F. Which is called a miss-and-hit topology on

• Báo cáo khoa học
• topological spaces
• Mathematics
• Physics
• Scientific reports
• scientific studies
• natural sciences
• Topological
• Simple vector spaces
• Lebesgue integral
• Normed spaces
• Banach spaces
• Metric Spaces
• Bounded Operators
• Topological complexity number
• Digital topology
• Digital topological complexity number
• Digital spaces
• Topological complexity number T C(X
• κ)
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• Invertible dynamical systems
• Li–Yorke chaos
• Noncompact spaces
• Topological conjugacy
• Hilbert space
• L fuzzy topology
• Qα compactness
• L fuzzy C closed set
• L fuzzy C continuous mappings
• L fuzzy net
• L fuzzy ideal
• C convergence
• Quotient space of a T space
• Generalized group
• Generalized action
• Quotient space
• Topological generalized groups
• Soft set
• Soft point
• Soft topological space
• Soft diagonal
• Soft uniform structure
• Soft uniform space
• Soft uniform continious function
• Quotient crossed module
• Double groupoid
• Quotient double groupoid
• Algebraic K theory
• Totally nonhomologous to zero
• Pro torus
• Fixed point
• Cohomological structure of a space
• Topological group
• N ary topological structures
• N ary open
• N ary closed
• N ary continuity
• Concept of binary topology
• Science and technology development
• The GAP function
• Parametric mixed strong vector quasivariational inequality problem
• The nonlinear scalarization function
• Hausdorff topological vector spaces
• Generalized Knaster Kuratowski Mazurkiewicz type theorems
• Applications to minimax inequalities
• L KKM mappings
• General topological spaces
• System vector quasi equilibrium problems
• Fixed point theorem
• Variational inequality problems
• Quasi equilibrium problems