[kisoron-ml] JAIST Logic Seminar Series

[Takako Nemoto]

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: t-nemoto at jaist.ac.jp
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*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