Аннотация:
Notions of $\mathcal{I}^\mathcal{K}$-Fréchet-Urysohn and $\mathcal{I}^\mathcal{K}$-sequential spaces are studied by letting ideals $\mathcal{I}$, $\mathcal{K}$ of subsets of natural numbers to play measurable role in the well-established concepts of Fréchet-Urysohn and sequential spaces. Relation among those spaces in new and old setting have been established by introducing $\mathcal{I}^\mathcal{K}$-quotient maps and $\mathcal{I}^\mathcal{K}$-covering maps.