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

## Quotient Vector Spaces and Functionals

Jaroslaw Kotowicz
University of Bialystok

### Summary.

The article presents well known facts about quotient vector spaces and functionals (see [8]). There are repeated theorems and constructions with either weaker assumptions or in more general situations (see [11], [7], [10]). The construction of coefficient functionals and non degenerated functional in quotient vector space generated by functional in the given vector space are the only new things which are done.

This work has been partially supported by TRIAL-SOLUTION grant IST-2001-35447 and SPUB-M grant of KBN.

#### MML Identifier: VECTSP10

The terminology and notation used in this paper have been introduced in the following articles [13] [5] [20] [12] [3] [1] [15] [2] [17] [7] [21] [4] [6] [14] [19] [18] [16] [9]

#### Contents (PDF format)

1. Auxiliary Facts about Double Loops and Vector Spaces
2. Quotient Vector Space for Non Commutative Double Loop
3. Auxiliary Facts about Functionals
4. Kernel of Additive Functional. Linear Functionals in Quotient Vector Spaces

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Received November 5, 2002