Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Introduction to Banach and Hilbert Spaces --- Part III
-
Jan Popiolek
-
Warsaw University, Bialystok
Summary.
-
The article is a continuation of [7] and
of [8].
First we define the following concepts: the Cauchy
sequence, the bounded sequence and the subsequence.
The last part of this article contains definitions
of the complete space and the Hilbert space.
MML Identifier:
BHSP_3
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[2]
[10]
[1]
[12]
[3]
[4]
[5]
[11]
[6]
[7]
[8]
Contents (PDF format)
Bibliography
- [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]
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]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Jan Popiolek.
Real normed space.
Journal of Formalized Mathematics,
2, 1990.
- [7]
Jan Popiolek.
Introduction to Banach and Hilbert spaces --- part I.
Journal of Formalized Mathematics,
3, 1991.
- [8]
Jan Popiolek.
Introduction to Banach and Hilbert spaces --- part II.
Journal of Formalized Mathematics,
3, 1991.
- [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [10]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [11]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
- [12]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received July 19, 1991
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