<abstract xmlns="http://www.w3.org/1999/xhtml">
<p><bold>Summary</bold>. 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 <monospace>TOP-REAL(n)</monospace>, <monospace>REAL-NS(n)</monospace>, and <monospace>n-VectSp over F Real</monospace>. We referred to [4], [9], and [8] in the formalization.</p>
</abstract>

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.

Real Vector Space and Related Notions

Formalized Mathematics

{"article-title":"Real Vector Space and Related Notions"}

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...

实向量空间及其相关概念

文章类别:冠词

在线发布:2021年12月30日

页面范围： 117 - 127

认可的:2021年6月30日

内政部： https://doi.org/10.2478/forma-2021-0012

关键词
实向量空间,拓扑空间,赋范空间

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