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In 2011, the theory of $\mathcal I^K$-convergence gets birth as an extensionof the concept of $\mathcal{I}^*$-convergence of sequences of real numbers.$\mathcal I^K$-limit points and $\mathcal I^K$-cluster points of functions areintroduced and studied to some extent, where $\mathcal{I}$ and $\mathcal{K}$are ideals on a non-empty set $S$. In a first countable space set of $\mathcalI^K$-cluster points is coincide with the closure of all sets in the filter base$\mathcal{B}_f(\mathcal{I^K})$ for some function $f : S\to X$. Frechetcompactness is studied in light of ideals $\mathcal{I}$ and $\mathcal{K}$ ofsubsets of $S$ and showed that in $\mathcal{I}$-sequential $T_2$ space Frechetcompactness and $\mathcal{I}$-Frechet compactness are equivalent. A class ofideals have been identified for which $\mathcal I^K$-Frechet compactnesscoincides with $\mathcal{I}$-Frechet compactness in first countable spaces.

$\mathcal I^K$-limit points, $\mathcal I^K$-cluster points and $\mathcal I^K$-Frechet compactness