# affine space

(redirected from Affine line)

## affine space

[ə′fīn ‚spās]
(mathematics)
An n-dimensional vector space which has an affine connection defined on it.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Then by Lemma 3.2, each affine line [L.sub.n] is an irreducible component of H.
Considering the projections of all ovals through x or y, except for X[x, y] itself, we obtain two sets of affine lines spanning [GAMMA] and such that each affine line of one set meets every affine line of the other set.
This firstly shows (V2) and secondly implies that the projections of [C.sub.1]\{x} and [C.sub.2]\{x} from the line <x, y> onto a solid [GAMMA] skew to <x, y> are two non-coplanar affine lines [A.sub.1] and [A.sub.2], respectively (an affine line is just the point set of a line with one point removed).
Trucco also proved several versions of Montel's theorem in a non-Archimedean setting and applied them to dynamics on the Berkovich projective and affine line in [FKT12].
Let Z be the affine line Spec k[[e.sub.1]], with the log structure associated to Q [right arrow] k[[e.sub.1]], [e.sub.1] [right arrow] [e.sub.1,], [e.sub.2] [right arrow] 0.
In the case when / = [f.sub.1].[f.sub.2]...[f.sub.d] and g = g1-g2...gd' where [f.sub.i] and [g.sub.j] are all of degree 1, then clearly we have that [C.sub.1] intersects [C.sub.2] in a maximum of d d' points which occurs when all affine lines [f.sub.i] = 0 intersect all affine lines [g.sub.j] at finite points.

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