Given a convex subset $X$ of a real vector space $V$, I'm interested in the set $$Y:=\{x\in X:\ \forall v\in V, \ \exists\epsilon>0 \text{ s.t. } x+\epsilon v \in Y \}.$$

My question is boring: Does $Y$ have a standard name?

I would be tempted to call it the "algebraic interior" of $X$ or the "geometric interior" of $X$, but I don't recall hearing these names before. Given just this structure, I feel like this is what I would assume somebody means if they referred to the interior of $X$, but my application of interest also has a topology sitting around, and I don't want to refer to the interior under that topology.