Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Real Normed Space

Jan Popiolek

Warsaw University, Bialystok

Supported by RPBP.III24.C8.
Summary.

We construct a real normed space $\langle V,~\Vert.\Vert\rangle$,
where $V$ is a real vector space and $\Vert.\Vert$ is a norm. Auxillary
properties of the norm are proved. Next, we introduce a notion
of sequence in the real normed space. The basic operations on
sequences (addition, subtraction, multiplication by real
number) are defined. We study some properties of sequences in
the real normed space and the operations on them.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[5]
[14]
[2]
[12]
[6]
[1]
[3]
[4]
[15]
[9]
[7]
[8]
[10]
[13]
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]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [13]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received September 20, 1990
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