A Proof of Constructive Version of Brouwer's Fixed Point Theorem with Uniform Sequential Continuity
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-09
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
It is often said that Brouwer's fixed point theorem cannot be constructively proved.
On the other hand, Sperner's lemma, which is used to prove Brouwer's theorem, can be constructively proved.
Some authors have presented a constructive (or an approximate) version of Brouwer's fixed point theorem using Sperner's lemma.
They, however, assume uniform continuity of functions.
We consider uniform sequential continuity of functions.
In classical mathematics, uniform continuity and uniform sequential continuity are equivalent.
In constructive mathematics a la Bishop, however, uniform sequential continuity is weaker than uniform continuity.
We will prove a constructive version of Brouwer's fixed point theorem in an n-dimensional simplex for uniformly sequentially continuous functions.
We follow the Bishop style constructive mathematics.
American Psychological Association (APA)
Tanaka, Yasuhito. 2011. A Proof of Constructive Version of Brouwer's Fixed Point Theorem with Uniform Sequential Continuity. ISRN Applied Mathematics،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-459613
Modern Language Association (MLA)
Tanaka, Yasuhito. A Proof of Constructive Version of Brouwer's Fixed Point Theorem with Uniform Sequential Continuity. ISRN Applied Mathematics No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-459613
American Medical Association (AMA)
Tanaka, Yasuhito. A Proof of Constructive Version of Brouwer's Fixed Point Theorem with Uniform Sequential Continuity. ISRN Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-459613
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459613