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

Contents (PDF format)

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

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