Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Real Normed Space

Jan Popiolek
Warsaw University, Bialystok
Supported by RPBP.III-24.C8.

Summary.

We construct a real normed space $\langle V,~\Vert.\Vert\rangle$, where $V$ is a real vector space and $\Vert.\Vert$ is a norm. Auxillary properties of the norm are proved. Next, we introduce a notion of sequence in the real normed space. The basic operations on sequences (addition, subtraction, multiplication by real number) are defined. We study some properties of sequences in the real normed space and the operations on them.

MML Identifier: NORMSP_1

The terminology and notation used in this paper have been introduced in the following articles [11] [5] [14] [2] [12] [6] [1] [3] [4] [15] [9] [7] [8] [10] [13]

Contents (PDF format)

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