Infinite -games with imperfect information
D. Blackwell (1969)
Applicationes Mathematicae
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D. Blackwell (1969)
Applicationes Mathematicae
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Salvador García-Ferreira, R. A. González-Silva, Artur Hideyuki Tomita (2002)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we deal with the product of spaces which are either -spaces or -spaces, for some . These spaces are defined in terms of a two-person infinite game over a topological space. All countably compact spaces are -spaces, and every -space is a -space, for every . We prove that if is a set of spaces whose product is a -space, then there is such that is countably compact for every . As a consequence, is a -space iff is countably compact, and if is a -space,...
C. A. Pensavalle, G. Pieri (2010)
Bollettino dell'Unione Matematica Italiana
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Consider a M-player game in strategic form where the set is a closed interval of real numbers and the payoff function is concave and differentiable with respect to the variable , for any . The aim of this paper is to find appropriate conditions on the payoff functions under the well-posedness with respect to the related variational inequality is equivalent to the formulation of the Tykhonov well-posedness in a game context. The idea of the proof is to appeal to a third equivalence,...
Tapani Hyttinen, Saharon Shelah, Jouko Vaananen (2002)
Fundamenta Mathematicae
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By results of [9] there are models and for which the Ehrenfeucht-Fraïssé game of length ω₁, , is non-determined, but it is consistent relative to the consistency of a measurable cardinal that no such models have cardinality ≤ ℵ₂. We now improve the work of [9] in two ways. Firstly, we prove that the consistency strength of the statement “CH and is determined for all models and of cardinality ℵ₂” is that of a weakly compact cardinal. On the other hand, we show that if , T is a countable...
Sergei Logunov (2001)
Commentationes Mathematicae Universitatis Carolinae
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We show, in particular, that every remote point of is a nonnormality point of if is a locally compact Lindelöf separable space without isolated points and .
Vladimir Vladimirovich Tkachuk (1997)
Commentationes Mathematicae Universitatis Carolinae
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A cardinal function (or a property ) is called -invariant if for any Tychonoff spaces and with and linearly homeomorphic we have (or the space has () iff ). We prove that the hereditary Lindelöf number is -invariant as well as that there are models of in which hereditary separability is -invariant.