Title: Ideal Cluster Points in Topological Spaces,
Abstract: Given an ideal $\mathcal{I}$ on $\omega$, we show that a sequence in a
topological space $X$ is $\mathcal{I}$-convergent if and only if there exists a
"big" $\mathcal{I}$-convergent subsequence. In addition, we study several
properties of $\mathcal{I}$-cluster points. As a consequence, the underlying
topology $\tau$ coincides with the topology generated by the pair
$(\tau,\mathcal{I})$. Then, we obtain two characterizations of the set of
$\mathcal{I}$-cluster points as classical cluster points of a filters on $X$
and as the smallest closed set containing "almost all" the sequence.