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More precisely, an affine space is a set with a free transitive vector space action. en.wikipedia.org

However, some one-dimensional subspaces are parallel to the affine space; in some sense, they intersect it at infinity. en.wikipedia.org

It can be thought of as a vector space (or affine space), a metric space, a topological space, a measure space, or a linear continuum. en.wikipedia.org

In an affine space, there are instead displacement vectors between two points of the space. en.wikipedia.org

Consider the line, which intersects the curve (inside affine space) exactly twice, namely in (1, 1) and (1, 1). en.wikipedia.org

In the second case, the tangent space is that line, considered as affine space. en.wikipedia.org

The conclusion is that any affine variety is a branched covering of affine space. en.wikipedia.org

Then the set complement is called an affine space. en.wikipedia.org

An affine space of positive dimension is not complete. en.wikipedia.org

Corresponding concept in an affine space is a convex set, which allows only convex combinations (non-negative linear combinations that sum to 1). en.wikipedia.org

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