  Given an ideal $\mathcal{I}$ on $\omega$ and a sequence $x$ in a topological
vector space, we let the $\mathcal{I}$-core of $x$ be the least closed convex
set containing $\{x_n: n \notin I\}$ for all $I \in \mathcal{I}$. We show two
characterizations of the $\mathcal{I}$-core. This implies that the
$\mathcal{I}$-core of a bounded sequence in $\mathbf{R}^k$ is simply the convex
hull of its $\mathcal{I}$-cluster points. As applications, we simplify and
extend several results in the context of Pringsheim-convergence and
$e$-convergence of double sequences.
