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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