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.III-24.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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