Definition:Affine Subspace
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Definition
Let $\EE$ be an affine space with tangent space $E$.
Let $\FF \subseteq \EE$ be a subset of $\EE$.
Then $\FF$ is an affine subspace of $\EE$ if and only if there exists a point $p \in \EE$ such that:
- $F_p := \set {q - p: q \in \FF}$
is a vector subspace of the vector space $E$.
Also known as
Some sources give this as affine manifold.
Also see
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): affine manifold (or affine subspace)
- 2006: Michèle Audin: Géométrie: I.2: Espaces affines
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): affine manifold (affine subspace)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): affine subspace