Kostyrko et al. initiated the concept of ideal convergence in [P. Kostyrko, T. Šalát, W. Wilczy ński, Real Anal. Exchange, 26 (2000), 669-686]. The purpose of this paper is to introduce and define spaces of the neutrosophic convergent sequence via ideal, namely I S M and I S M 0 . We prove that new spaces are linear and Hausdorff topological spaces. Further, we examine the relation between I-Cauchy and I-convergent sequences and show that every separable space I S M is second countable. Moreover, we prove that the space I S M is complete.
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