We first introduce a new notion called statistical convergence of order α and primarily show that it gives rise to a decreasing chain of closed linear subspaces of the space of all bounded real sequences with sup norm which never coincides with the class of convergent sequences and in fact their intersection properly contains the class of convergent sequences. We then show that the same method can be applied for double sequences also and introduce the notion of statistical convergence of order (α, β).
<p> In this paper we introduce the concept of ideal sequence covering map which is a generalization of sequence covering map, and investigate some of its properties. The present article contributes to the problem of characterization to the certain images of metric spaces which posed by Y. Tanaka [22], in more general form. The entire investigation is performed in the setting of ideal convergence extending the recent results in [11,15,16]. </p>
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