In this paper, we investigate some properties of sequences in a gradual normed space. We define some new notions such as gradual convergent sequences, gradual Cauchy sequences, etc., and then we state some theorems about these notions. Finally, in the last section, we bring some illustrative examples.

In this paper, we have investigated some topological properties of sets in a given gradual normed space. We have stated gradual Hausdorff property and then,we have studied the relationship between gradual closed sets and gradual compact sets. Also, we have given a result about having the closure point for an innite set in a gradual normed space. In the end, we have provided some illustrative examples.

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