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The Bolzano-Poincaré Type Theorems
Joint Authors
Turzański, Marian
Tkacz, Przemysław
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-12
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In 1883–1884, Henri Poincaré announced the result about the structure of the set of zeros of function f : In→Rn, or alternatively the existence of solutions of the equation f(x)=0.
In the case n=1 the Poincaré Theorem is well known Bolzano Theorem.
In 1940 Miranda rediscovered the Poincaré Theorem.
Except for few isolated results it is essentially a non-algorithmic theory.
The aim of this article is to introduce an algorithmical proof of the Theorem “On the existence of a chain” and for n=3 an algorithmical proof of the Bolzano-Poincaré Theorem and to show the equivalence of Poincaré, Brouwer and “On the existence of a chain” theorems.
American Psychological Association (APA)
Tkacz, Przemysław& Turzański, Marian. 2011. The Bolzano-Poincaré Type Theorems. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-498617
Modern Language Association (MLA)
Tkacz, Przemysław& Turzański, Marian. The Bolzano-Poincaré Type Theorems. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-498617
American Medical Association (AMA)
Tkacz, Przemysław& Turzański, Marian. The Bolzano-Poincaré Type Theorems. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-498617
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-498617