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

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

The following notions are introduced in the article: subspace of a
real linear space, zero subspace and improper subspace, coset of a subspace.
The relation of a subset of the vectors being linearly closed is also
introduced.
Basic theorems concerning those notions are proved in the article.
MML Identifier:
RLSUB_1
The terminology and notation used in this paper have been
introduced in the following articles
[4]
[3]
[8]
[6]
[5]
[1]
[9]
[2]
[7]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [5]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [7]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received July 24, 1989
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