The fan theorem
نویسنده
چکیده
منابع مشابه
Fan-KKM Theorem in Minimal Vector Spaces and its Applications
In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.
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This article presents a formulation of the fan theorem in Martin-Löf’s type theory. Starting from one of the standard versions of the fan theorem we gradually introduce reformulations leading to a final version which is easy to interpret in type theory. Finally we describe a formal proof of that final version of the fan theorem.
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It is often demonstrated that Brouwer’s fixed point theorem can not be constructively proved. Therefore, Kakutani’s fixed point theorem, the Fan-Glicksberg fixed point theorem and the existence of a pure strategy Nash equilibrium in a strategic game with continuous (infinite) strategies and quasi-concave payoff functions also can not be constructively proved. On the other hand, however, Sperner...
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The objective of this paper is the numerical study of the flow through an axial fan and examining the effects of blade design parameters on the performance of the fan. The axial fan is extensively used for cooling of the electronic devices and servers. Simulation of the three-dimensional incompressible turbulent flow was conducted by numerical solution of the (RANS) equations for a model. The S...
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We introduce axioms LFAN and CFAN , where the former follows from the law of excluded middle and the latter follows from the axiom of countable choice. Then we show that Brouwer’s fan theorem is constructively equivalent to LFAN + CFAN . This decomposition of the fan theorem into a logical axiom and a function existence axiom contributes to the programme of constructive reverse mathematics. 200...
متن کاملRecent Applications of the Fan-kkm Theorem
In this review, firstly, we recall Ky Fan’s contributions to the KKM theory based on his celebrated 1961 KKM lemma (or the Fan-KKM theorem). Secondly, we introduce relatively recent applications of the Fan lemma due to other authors in the 21st century. Finally, some historical remarks on related works are added.
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تاریخ انتشار 2017