共查询到20条相似文献,搜索用时 31 毫秒
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《Nonlinear Analysis: Theory, Methods & Applications》2004,57(2):173-181
Let be a measurable space, X and Y separable Banach spaces, and C a weakly compact subset of X. Let and be continuous random operators. Then the deterministic solvability of the equationimplies the stochastic solvability of it provided that (f−T)(ω,.) is demiclosed at zero and T(ω,C) is bounded for each . As applications, random fixed points of various types of pseudo-contractive and k-set-contractive random operators are obtained. 相似文献
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In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems. 相似文献
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《Topology and its Applications》2004,135(1-3):231-247
A topological system (X,f) is -transitive if for each pair of opene subsets U and V of X, , where is a collection of subsets of which is hereditary upward. (X,f) is -mixing if (X×X,f×f) is -transitive. In this paper -mixing systems are characterized in terms of the chaoticity of the systems. Moreover, weak disjointness is studied via family. We will give conditions such that a dual theorem of the Weiss–Akin–Glasner theorem holds. Examples with this dual theorem fails for some “good” families are obtained. 相似文献
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Philip Kremer 《Archive for Mathematical Logic》2006,45(8):1021-1032
Let
be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality
and a temporal modality
, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language
by interpreting
in dynamic topological systems, i.e. ordered pairs
, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result. 相似文献
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Let be two commuting continuous maps. We establish some results on the topological dynamic shared by both maps and state some conditions to get that the topological entropy of the composition f○g will be positive. 相似文献
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R.Grant Woods 《Topology and its Applications》1985,21(3):287-295
Let be a closed-hereditary topological property preserved by products. Call a space -regular if it is homeomorphic to a subspace of a product of spaces with . Suppose that each -regular space possesses a -regular compactification. It is well-known that each -regular space X is densely embedded in a unique space γscPX with such that if f: X → Y is continuous and Y has , then f extends continuously to γscPX. Call -pseudocompact if γscPX is compact.Associated with is another topological property #, possessing all the properties hypothesized for above, defined as follows: a -regular space X has # if each -pseudocompact closed subspace of X is compact. It is known that the -pseudocompact spaces coincide with the #-pseudocompact spaces, and that # is the largest closed-hereditary, productive property for which this is the case. In this paper we prove that if is not the property of being compact and -regular, then # is not simply generated; in other words, there does not exist a space E such that the spaces with # are precisely those spaces homeomorphic to closed subspaces of powers of E. 相似文献
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Philip Kremer 《Archive for Mathematical Logic》2010,49(4):519-527
Let
L\square°{{\mathcal L}^{\square\circ}} be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality □ and a
temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language
L\square°{{\mathcal L}^{\square\circ}} by interpreting
L\square°{{\mathcal L}^{\square\circ}} in dynamic topological systems, i.e., ordered pairs 〈X, f〉, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown that S4C is sound and complete for this semantics.
S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fernández
Duque); but incomplete for continuous functions on the real line (Kremer and Mints, Slavnov). Here we show that S4C is complete
for continuous functions on the rational numbers. 相似文献
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Harald Brandenburg 《Topology and its Applications》1985,20(1):17-27
Following Pareek a topological space X is called D-paracompact if for every open cover of X there exists a continuous mapping f from X onto a developable T1-space Y and an open cover of Y such that { f-1[B]|B ∈ } refines . It is shown that a space is D-paracompact if and only if it is subparacompact and D-expandable. Moreover, it is proved that D-paracompactness coincides with a covering property, called dissectability, which was introduced by the author in order to obtain a base characterization of developable spaces. 相似文献
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Philippe Bich 《Comptes Rendus Mathematique》2004,338(9):673-678
In this article, we extend Brouwer's fixed point theorem – which states that every continuous mapping (a closed ball of ) must have a fixed point – by allowing discontinuities of f, and we apply this extension to equilibrium theory in Economics. To cite this article: P. Bich, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
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Ulrich Höhle 《Journal of Mathematical Analysis and Applications》1980,78(2):659-673
Let (X, τ) be a generalized topological space of type α (see A. Appert and K. Fan, “Espaces topologiques intermédiares,” Herman, Paris, 1951) and (L, ?) be a complete Brouwerian lattice such that the dual lattice of (L, ?) is also Brouwerian. We prove that every upper semicontinuous L-fuzzy subset of X can be represented by a τ-closed random set. As an important application we obtain a fuzzification of measurable spaces as well as of topological spaces. In particular a concept of measurable (open) L-fuzzy sets is developed. 相似文献
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Let be a smooth bounded domain in . Assume f∈C1[0,∞) is a non-negative function such that f(u)/u is increasing on (0,∞). Let a be a real number and let b?0, be a continuous function such that b≡0 on . We study the logistic equation Δu+au=b(x)f(u) in . The special feature of this work is the uniqueness of positive solutions blowing-up on , in a general setting that arises in probability theory. To cite this article: F.-C. C??rstea, V. R?dulescu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 447–452. 相似文献