Journal of Formalized Mathematics
Volume 7, 1995
University of Bialystok
Copyright (c) 1995
Association of Mizar Users
The Cantor Set

Alexander Yu. Shibakov

The Ural University, Ekaterinburg

Andrzej Trybulec

Warsaw University, Bialystok
Summary.

The aim of the paper is to define some basic notions of the theory
of topological spaces like basis and prebasis, and to prove their
simple properties. The definition of the Cantor set is given in terms
of countable product of $\{0,1\}$ and a collection of its subsets
to serve as a prebasis.
The present work had been completed while the first author's visit to
Bia{\l}ystok in winter 199495.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[4]
[12]
[11]
[7]
[13]
[2]
[3]
[6]
[8]
[5]
[1]
[9]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
K\"onig's theorem.
Journal of Formalized Mathematics,
2, 1990.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [11]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received January 9, 1995
[
Download a postscript version,
MML identifier index,
Mizar home page]