1. bookVolume 29 (2021): Issue 3 (October 2021)
Journal Details
License
Format
Journal
eISSN
1898-9934
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English
access type Open Access

Real Vector Space and Related Notions

Published Online: 30 Dec 2021
Volume & Issue: Volume 29 (2021) - Issue 3 (October 2021)
Page range: 117 - 127
Accepted: 30 Jun 2021
Journal Details
License
Format
Journal
eISSN
1898-9934
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English

Summary. In this paper, we discuss the properties that hold in finite dimensional vector spaces and related spaces. In the Mizar language [1], [2], variables are strictly typed, and their type conversion requires a complicated process. Our purpose is to formalize that some properties of finite dimensional vector spaces are preserved in type transformations, and to contain the complexity of type transformations into this paper. Specifically, we show that properties such as algebraic structure, subsets, finite sequences and their sums, linear combination, linear independence, and affine independence are preserved in type conversions among TOP-REAL(n), REAL-NS(n), and n-VectSp over F Real. We referred to [4], [9], and [8] in the formalization.

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MSC

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