Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Operations on Subspaces in Real Linear Space

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

In this article the following operations on subspaces of real linear space
are intoduced: sum, intersection and direct sum. Some theorems about those
notions are proved. We define linear complement of a subspace.
Some theorems about decomposition of a vector onto two subspaces
and onto subspace and its linear complement are proved.
We also show that a set of subspaces with operations sum and intersection
is a lattice.
At the end of the article theorems that belong rather to [4],
[8], [7] or [12] are proved.
MML Identifier:
RLSUB_2
The terminology and notation used in this paper have been
introduced in the following articles
[6]
[3]
[9]
[1]
[10]
[2]
[12]
[11]
[8]
[7]
[5]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Library Committee.
Boolean properties of sets  requirements.
Journal of Formalized Mathematics,
EMM, 2002.
 [5]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [7]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Stanislaw Zukowski.
Introduction to lattice theory.
Journal of Formalized Mathematics,
1, 1989.
Received September 20, 1989
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