Volume 3, 1991

University of Bialystok

Copyright (c) 1991 Association of Mizar Users

**Agata Darmochwal**- Warsaw University, Bialystok
- The article was written during my work at Shinshu University, 1991.
**Yatsuka Nakamura**- Shinshu University, Nagano

- Heine-Borel's covering theorem, also known as Borel-Lebesgue theorem ([5]), is proved. Some useful theorems about real inequalities, intervals, sequences and notion of power sequence which are necessary for the theorem are also proved.

Contents (PDF format)

- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Grzegorz Bancerek.
Sequences of ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Leszek Borys.
Paracompact and metrizable spaces.
*Journal of Formalized Mathematics*, 3, 1991. - [5] Nicolas Bourbaki. \em Elements de Mathematique, volume Topologie Generale. HERMANN, troisieme edition edition, 1960.
- [6]
Czeslaw Bylinski.
Binary operations.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Agata Darmochwal.
Compact spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Agata Darmochwal and Yatsuka Nakamura.
Metric spaces as topological spaces --- fundamental concepts.
*Journal of Formalized Mathematics*, 3, 1991. - [11]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Jaroslaw Kotowicz.
The limit of a real function at infinity.
*Journal of Formalized Mathematics*, 2, 1990. - [15]
Rafal Kwiatek.
Factorial and Newton coefficients.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Jan Popiolek.
Some properties of functions modul and signum.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Konrad Raczkowski and Andrzej Nedzusiak.
Real exponents and logarithms.
*Journal of Formalized Mathematics*, 2, 1990. - [19]
Konrad Raczkowski and Pawel Sadowski.
Topological properties of subsets in real numbers.
*Journal of Formalized Mathematics*, 2, 1990. - [20]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [21]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [22]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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