On n-Frechet spaces

In this paper, we introduce the notion of n-sequential closure operators and use these operators to construct classes of n-Frechet spaces as generalizations of the class of Frechet spaces. Then we get some necessary and sufficiency conditions for a sequential space to be a Frechet space. These results are generalizations of the preceding one of W. C. Hong in [5]. Keywords Frechet, n-Frechet, sequential, sequential closure, n-sequential closure.
[section]1. Introduction and results M. Venkataraman poses the following problem in [8]. Problem 1.1. Characterize "the class of topological spaces which can be specified completely by knowledge of their convergent [...]