Can someone unpack the definition of an affine subspace for me, it's been a while since I took point set topology:
A subset U ⊂ V of a vector space V is an affine space if there exists a u ∈ U such that U - u = {x - u | x ∈ U} is a vector subspace of V.
I'm unpacking this to read
A subset U of a vector space of V is an affine space if there exists an element u such that U - u, which is exactly equal to x - u for all x in U, is a vector subspace of V.
If I'm reading that right, the right side of the equation is a paranthetic expression, so is it necessary?
A subset U ⊂ V of a vector space V is an affine space if there exists a u ∈ U such that U - u = {x - u | x ∈ U} is a vector subspace of V.
I'm unpacking this to read
A subset U of a vector space of V is an affine space if there exists an element u such that U - u, which is exactly equal to x - u for all x in U, is a vector subspace of V.
If I'm reading that right, the right side of the equation is a paranthetic expression, so is it necessary?