Understanding the symbol <A,B> in affine spaces

Question

I'm trying to solve this exercise:

A subset F of an affine space is an affine subspace if and only if for all points A and B of F, the inclusion <A, B> ⊂ F holds.

However, i don't understand what <A, B> is intended to represent in this context, can you explain me ?

Thanks

Answer 1

For two points, the notation $\langle A, B\rangle$ means the line through those points. Explicitly, we have

$$\langle A,B \rangle = \{tA+(1-t)B : t \in \mathbb{R}\}$$