皆様
Ludwig-Maximilians-Universität München の Josef Berger 博士の講演のお知らせです。 どうぞふるってご参加ください。
問い合わせ先： 根元 多佳子 北陸先端科学技術大学院大学 情報科学系 email: [email protected] ---------------------------------------------
*JAIST Logic Seminar Series*
Date: Thursday 16 March, 2017, 15:20-17:00
Place: JAIST, Collaboration room 7 (I-56) (Access: http://www.jaist.ac.jp/english/location/access.html)
Speaker: Josef Berger (udwig-Maximilians-Universität München, Germany) (joint work with Gregor Svindland)
Brouwer's fan theorem and convexity
In the framework of Bishop's constructive mathematics, we introduce a correspondence between sets B of finite binary sequences on the one hand and uniformly continuous functions f on the unit interval on the other hand. This correspondence is compatible with basic properties of the involved objects as follows: i) B is a bar if and only if the corresponding f is positive-valued ii) B is a uniform bar if and only if f has positive infimum iii) B is weakly convex if and only f is weakly convex.
This simplifies and generalises a result in
William H. Julian and Fred Reichmann, A uniformly continuous function on [0, 1] that is everywhere different from its infimum. Pacific Journal of Mathematics 111, No 2 (1984) 333–340