<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, we formalize in Mizar [1], [2] the 3-fold product space of real normed spaces for usefulness in application fields such as engineering, although the formalization of the 2-fold product space of real normed spaces has been stored in the Mizar Mathematical Library [3].</p>
<p>First, we prove some theorems about the 3-variable function and 3-fold Cartesian product for preparation. Then we formalize the definition of 3-fold product space of real linear spaces. Finally, we formulate the definition of 3-fold product space of real normed spaces. We referred to [7] and [6] in the formalization.</p>
</abstract>

In this article, we formalize in Mizar [1], [2] the 3-fold product space of real normed spaces for usefulness in application fields such as engineering, although the formalization of the 2-fold product space of real normed spaces has been stored in the Mizar Mathematical Library [3].
First, we prove some theorems about the 3-variable function and 3-fold Cartesian product for preparation. Then we formalize the definition of 3-fold product space of real linear spaces. Finally, we formulate the definition of 3-fold product space of real normed spaces. We referred to [7] and [6] in the formalization.

The 3-Fold Product Space of Real Normed Spaces and its Properties

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"The 3-Fold Product Space of Real Normed Spaces and its Properties"}

In this article, we formalize in Mizar [1], [2] the 3-fold product space of real normed spaces for usefulness in application fields such as engineering,...

The 3-Fold Product Space of Real Normed Spaces and its Properties

Published Online: Jul 09, 2022

Page range: 241 - 248

Accepted: Nov 30, 2021

DOI: https://doi.org/10.2478/forma-2021-0022

Keywords
3-fold product spaces, linear spaces, normed spaces

© 2022 Hiroyuki Okazaki et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

The 3-Fold Product Space of Real Normed Spaces and its Properties

Published Online: Jul 09, 2022

Page range: 241 - 248

Accepted: Nov 30, 2021

DOI: https://doi.org/10.2478/forma-2021-0022

Keywords3-fold product spaces, linear spaces, normed spaces

© 2022 Hiroyuki Okazaki et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
3-fold product spaces, linear spaces, normed spaces