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Cantor Set and its properties

Authors

DOI:

https://doi.org/10.35819/remat2021v7i1id4394

Keywords:

Cantor Set, Countable Sets, Homeomorphic Sets, Topolical Notions on the Real Line

Abstract

This work intends to publicize the already well-known Cantor set. The idea is to show a more detailed demonstration of some important properties that it has, in a certain way being not very common to find in texts in Portuguese. We will also see that, except for homeomorphism, the Cantor Set is the only one, as metric space, with all the indicated properties.

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Author Biographies

References

BROUWER, L. E. J. On the structure of perfect sets of points. KNAW, Proceedings, v. 23, n. 4, p. 397-399, 1910.

FREIRA, A. A. A teoria dos conjuntos de cantor. Paidéia, Ribeirão Preto, n. 2, fev./jul. 1992. DOI: https://doi.org/10.1590/S0103-863X1992000200008.

IMPA. Instituto de Matemática Pura e Aplicada. Georg Cantor (1845-1918) - pai do infinito e do ICM. 15 dez. 2017. Disponível em: https://impa.br/noticias/georg-cantor-1845-1918-pai-do-infinito-e-do-icm/. Acesso em: 06 jun. 2020.

LIMA, E. L. Análise Real. v. 1, 12. ed. Rio de Janeiro:

IMPA, 2018.

LIMA, E. L. Curso de Análise. v. 2, 11. ed. Rio de Janeiro: IMPA, 2014.

MATHONLINE. Compact Sets in a Metric Space are Closed and Bounded. Disponível em: http://mathonline.wikidot.com/compact-sets-in-a-metric-space-are-closed-and-bounded. Acesso em: 23 jun. 2020.

MUNKRES, J. R. Topology. 2. ed. New Jersey: Prentice Hall, 2000.

WILLARD, S. General Topology. Mineola N. Y.: Dover Publications, 2004.

Published

2021-04-20

Versions

Issue

Section

Mathematics

How to Cite

ASSUNÇÃO, Bryan Douglas Nunes; BERTOLOTO, Fábio José. Cantor Set and its properties. REMAT: Revista Eletrônica da Matemática, Bento Gonçalves, RS, Brasil, v. 7, n. 1, p. e3011, 2021. DOI: 10.35819/remat2021v7i1id4394. Disponível em: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4394. Acesso em: 20 jun. 2026.