Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Subspaces and Cosets of Subspace of Real Unitary Space


Noboru Endou
Gifu National College of Technology
Takashi Mitsuishi
Miyagi University
Yasunari Shidama
Shinshu University, Nagano

Summary.

In this article, subspace and the coset of subspace of real unitary space are defined. And we discuss some of their fundamental properties.

MML Identifier: RUSUB_1

The terminology and notation used in this paper have been introduced in the following articles [6] [3] [11] [8] [7] [1] [12] [2] [5] [10] [9] [4]

Contents (PDF format)

  1. Definition and Axioms of the Subspace of Real Unitary Space
  2. Definition of Zero Subspace and Improper Subspace of Real Unitary Space
  3. Theorems of Zero Subspace and Improper Subspace
  4. The Cosets of Subspace of Real Unitary Space
  5. Theorems of the Cosets

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] Jan Popiolek. Introduction to Banach and Hilbert spaces --- part I. Journal of Formalized Mathematics, 3, 1991.
[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] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[9] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.
[10] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received October 9, 2002


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