共查询到20条相似文献,搜索用时 15 毫秒
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Petr Holicky 《Proceedings of the American Mathematical Society》2006,134(5):1519-1525
We prove that every (extended) Borel subset of , where is a complete metric and is Polish, can be covered by countably many extended Borel graphs of mappings from to if the sections , , are countable. This is a nonseparable version of a classical theorem of Luzin and Novikov.
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Ali Rezaei Aliabad 《Czechoslovak Mathematical Journal》2006,56(4):1193-1206
Let {X α } α∈Λ be a family of topological spaces and x α ∈ X α , for every α ∈ Λ. Suppose X is the quotient space of the disjoint union of X α ’s by identifying x α ’s as one point σ. We try to characterize ideals of C(X) according to the same ideals of C(X α )’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let m be an infinite cardinal. (1) Is there any ring R and I an ideal in R such that I is an irreducible intersection of m prime ideals? (2) Is there any set of prime ideals of cardinality m in a ring R such that the intersection of these prime ideals can not be obtained as an intersection of fewer than m prime ideals in R? Finally, we answer an open question in [11]. 相似文献
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Dale Myers 《Algebra Universalis》1992,29(4):589-600
We construct two Boolean spaces with countable bases which have continuum many orbits. Two points are in the same orbit iff there is a homeomorphism of the space which carries one to the other. One of our examples is a primitive Boolean space. J. Donald Monk posed these problems. We don't know if there is a countably based Boolean space with exactly 1 orbits.Presented by R. S. Pierce. 相似文献
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The construct M of metered spaces and contractions is known to be a superconstruct in which all metrically generated constructs can be fully embedded. We show that M has one point extensions and that quotients in M are productive. We construct a Cartesian closed topological extension of M and characterize the canonical function spaces with underlying sets Hom(X,Y) for metered spaces X and Y. Finally we obtain an internal characterization of the objects in the Cartesian closed topological hull of M. 相似文献
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Andrzej S. Nowak 《Mathematical Methods of Operations Research》1999,50(1):65-76
We consider stochastic games with countable state spaces and unbounded immediate payoff functions. Our assumptions on the transition structure of the game are based on a recent work by Meyn and Tweedie [19] on computable bounds for geometric convergence rates of Markov chains. The main results in this paper concern the existence of sensitive optimal strategies in some classes of zero-sum stochastic games. By sensitive optimality we mean overtaking or 1-optimality. We also provide a new Nash equilibrium theorem for a class of ergodic nonzero-sum stochastic games with denumerable state spaces. 相似文献
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Winfried Just Ol'ga V. Sipacheva Paul J. Szeptycki 《Proceedings of the American Mathematical Society》1996,124(4):1227-1235
Examples of spaces are constructed for which is not normal but all closed discrete subsets are countable. A monolithic example is constructed in ZFC and a separable first countable example is constructed using .
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Michel C Delfour 《Journal of Mathematical Analysis and Applications》1973,42(3):554-568
Vector spaces of functions and equivalence classes of functions for which a natural projective limit structure exists are studied in a systematic manner. The theory is illustrated by a series of examples arising from specific applications to the stability of feedback systems and the theory of hereditary differential systems. 相似文献
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Juan Jorge Schäffer 《Mathematische Annalen》1959,137(3):209-262
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We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ). 相似文献
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A. A. Lykov 《Moscow University Mathematics Bulletin》2013,68(4):202-205
Upper and lower bounds for the expected first passage time of a distant point are obtained for ergodic countable Markov chains in terms of Lyapunov function and stationary distribution. 相似文献
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Let T be a tent map with the slope strictly between and 2. Suppose that the critical point of T is not recurrent. Let K denote the inverse limit space obtained by using T repeatedly as the bonding map. We prove that every homeomorphism of K to itself is isotopic to some power of the natural shift homeomorphism. 相似文献
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Paul J. Szeptycki 《Topology and its Applications》2010,157(9):1622-1628
The class of normal spaces that have normal product with every countable space is considered. A countably compact normal space X and a countable Y such that X×Y is not normal is constructed assuming CH. Also, ? is used to construct a perfectly normal countably compact X and a countable Y such that X×Y is not normal. The question whether a Dowker space can have normal product with itself is considered. It is shown that if X is Dowker and contains any countable non-discrete subspace, then X2 is not normal. It follows that a product of a Dowker space and a countable space is normal if and only if the countable space is discrete. If X is Rudin's ZFC Dowker space, then X2 is normal. An example of a Dowker space of cardinality ℵ2 with normal square is constructed assuming . 相似文献
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Let G be a finite group, F a field, and V a finite dimensional FG-module such that G has no trivial composition factor on V. Then the arithmetic average dimension of the fixed point spaces of elements of G on V is at most where p is the smallest prime divisor of the order of G. This answers and generalizes a 1966 conjecture of Neumann which also appeared in a paper of Neumann and Vaughan-Lee and also as a problem in The Kourovka Notebook posted by Vaughan-Lee. Our result also generalizes a recent theorem of Isaacs, Keller, Meierfrankenfeld, and Moretó. We also classify precisely when equality can occur. Various applications are given. For example, another conjecture of Neumann and Vaughan-Lee is proven and some results of Segal and Shalev are improved and/or generalized concerning BFC groups. 相似文献