Pesquisas e Relatórios sobre Matemática

On Statistically (I) - Sequential Spaces

Renukadeviz V and Prakash B

In this paper, we answer the question “Is the product of two statistically sequential spaces statistically sequential?” raised by Zhongbao and Fucai. By an example we see that products of two statistically sequential spaces need not be statistically sequential. Also, we give a necessary and sufficient condition for the product to be in most general case of I-sequential spaces. And we point out the error in proposition 2.2 of. Further, we prove that a subspace of a statistically sequential space need not be statistically sequential and we find a necessary and sufficient condition for a subspace to be in most general case of an I-sequential space. Finally, we develop the properties of the most general concept of I-sequential spaces.