Un estudio sistemático del teorema de Tychonoff
El objetivo central de este trabajo es realizar un estudio sistemático del teorema de Tychonoff, analizando distintas demostraciones del teorema, que surgieron al pasar el tiempo, y mostrando además su equivalencia con el axioma de elección. Presentamos distintas demostraciones del teorema objeto de...
- Autores:
-
Quintanilla Gonzalez, Brayan Gersain
- Tipo de recurso:
- http://purl.org/coar/version/c_b1a7d7d4d402bcce
- Fecha de publicación:
- 2016
- Institución:
- Universidad Industrial de Santander
- Repositorio:
- Repositorio UIS
- Idioma:
- spa
- OAI Identifier:
- oai:noesis.uis.edu.co:20.500.14071/35522
- Palabra clave:
- Teorema De Tychonoff
Teorema De Tychonoff Equivalente Al Axioma De Elección
Teorema De Los Productos Conexos
Compacto
Conexo.
The central objective of this work is to perform a systematic study of Tychonoff’s theorem
analyzing different proofs of the theorem
which emerged over time
and also showing its equivalence to the axiom of choice. We present different demonstrations of the theorem object of study of our work. These demonstrations make use of different “ tools ”. We also analyze the publication of J. L. Kelley [5]
in which it “demonstrates” the equivalence of Tychonoff’s theorem and the axiom of choice. Kelley makes a small mistake in his test
which is mentioned in [7]
but until the year 2003
Sangho Kum [6] corrects and publishes. On the other hand
we find the article [10] of J. A. P´erez
in which the author intends to show that the theorem of connected products is equivalent to Tychonoff’s theorem and hence to the axiom of choice. However when studying this article we find an error in the proof of the main theorem. In this last chapter we present a summary of what happened around this situation. We hope that this thesis will be of interest and useful to students of mathematics
bachelors in mathematics and in general for any reader interested in the subject.
- Rights
- License
- Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)