✦ LIBER ✦

On the definition of isomorphisms of linear spaces

✍ Scribed by Alexander Kreuzer

Publisher: Springer
Year: 1996
Tongue: English
Weight: 221 KB
Volume: 61
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00150028

No coin nor oath required. For personal study only.

✦ Synopsis

Let (P, ~) and (P', ~') be linear spaces satisfying the exchange axiom with dim P = dim P' E N. Then a bijection ~: P ---, P' which maps collinear points onto collinear points is an isomorphism. Also a surjection ~b: P ---. P' which maps any three non-collinear points to noncollinear points is an isomorphism. This assertion is not true if dim P is not finite.

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