Ideal convergence in a topological space is induced by changing the definition of the convergence of sequences on the space by an ideal. Let I⊆2N\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {I}}\subseteq 2^{\mathbb {N}}$$\end{document} be an ideal. A sequence (xn:n∈N)\documentclass[12pt]{minimal}
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\begin{document}$$(x_{n}:n\in {\mathbb {N}})$$\end{document} in a topological space X is said to be I\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal I$$\end{document}-convergent to a point x∈X\documentclass[12pt]{minimal}
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\begin{document}$$x\in X$$\end{document} provided for any neighborhood U of x in X, we have the set {n\documentclass[12pt]{minimal}
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\begin{document}$$\{n$$\end{document}∈N:xn∉U}∈I\documentclass[12pt]{minimal}
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\begin{document}$$\in {\mathbb {N}}:x_{n}\notin U \}\in {\mathcal {I}}$$\end{document}. Recently, I\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {I}}$$\end{document}-sequential spaces and I\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {I}}$$\end{document}-Fréchet-Urysohn spaces are introduced and studied. In this paper, we discuss some topological spaces defined by I\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {I}}$$\end{document}-convergence and their mappings on these spaces, expound their operation properties on these spaces, and study the role of maximal ideals of N\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {N}}$$\end{document} in I\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal I$$\end{document}-convergence. We can apply I\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {I}}$$\end{document}-convergence to unify and simplify the proofs of some old results in the literature and obtain some new results on the usual convergence and statistical convergence of topological spaces.
