Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

## Projections in $n$-Dimensional Euclidean Space to Each Coordinates

Roman Matuszewski
University of Bialystok
The work was done, while the author stayed at Nagano in the fall of 1996.
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

In the $n$-dimensional Euclidean space ${\cal E}^n_{\rm T}$, a projection operator to each coordinate is defined. It is proven that such an operator is linear. Moreover, it is continuous as a mapping from ${\cal E}^n_{\rm T}$ to ${R}^{1}$, the carrier of which is a set of all reals. If $n$ is 1, the projection becomes a homeomorphism, which means that ${\cal E}^1_{\rm T}$ is homeomorphic to ${R}^{1}$.

#### MML Identifier: JORDAN2B

The terminology and notation used in this paper have been introduced in the following articles [22] [27] [2] [24] [16] [1] [26] [10] [21] [28] [3] [12] [7] [8] [6] [25] [4] [15] [14] [20] [23] [17] [13] [18] [9] [19] [11] [5]

#### Contents (PDF format)

1. Projections
2. Continuity of Projections
3. 1-dimensional and 2-dimensional Cases

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Received November 3, 1997