Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Sequences in Metric Spaces

Stanislawa Kanas

Technical University of Rzeszow

Adam Lecko

Technical University of Rzeszow
Summary.

Sequences in metric spaces are defined.
The article contains definitions of bounded, convergent, Cauchy
sequences. The subsequences are introduced too.
Some theorems concerning sequences are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[15]
[5]
[17]
[1]
[16]
[12]
[18]
[3]
[4]
[7]
[8]
[11]
[9]
[10]
[2]
[6]
[13]
[14]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Leszek Borys.
Paracompact and metrizable spaces.
Journal of Formalized Mathematics,
3, 1991.
 [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Alicia de la Cruz.
Totally bounded metric spaces.
Journal of Formalized Mathematics,
3, 1991.
 [7]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
Journal of Formalized Mathematics,
2, 1990.
 [9]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Jan Popiolek.
Real normed space.
Journal of Formalized Mathematics,
2, 1990.
 [14]
Jan Popiolek.
Introduction to Banach and Hilbert spaces  part III.
Journal of Formalized Mathematics,
3, 1991.
 [15]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [16]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [17]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [18]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received December 12, 1991
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