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In this paper, we consider certain topological properties along with certaintypes of mappings on these spaces defined by the notion of ideal convergence.In order to do that, we primarily follow in the footsteps of the earlierstudies of ideal convergence done by using functions (from an infinite set $S$to $X$) in \cite{CS, das4, das5}, as that is the most general perspective anduse functions instead of sequences/nets/double sequences etc. This functionalapproach automatically provides the most general settings for such studies andconsequently extends and unifies the proofs of several old and recent resultsin the literature about spaces like sequential, Fr\'{e}chet-Uryshon spaces andsequential, quotient and covering maps. In particular, we introduce andinvestigate the notions of $\ic$-functional spaces, $\ic$-functionalcontinuous, quotient and covering mappings and finally $\ic$-functionalFr\'{e}chet-Uryshon spaces. In doing so, we take help of certain set theoreticand other properties of ideals.

On certain generalized notions using $\mathcal{I}$-convergence in topological spaces