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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