About sequentially open and closed subsets in product spaces

Abstract

We remind two facts for topological spaces. The one is that in a Hausdorff space $X$ each sequence has a unique limit. This allows us to have a function from the set of all sequences in $X$ to $X$. Another is that in the first countable spaces some topological objects such as open subsets, closed subsets, closures and interiors of the sets, continuous functions and many others can be defined in terms of convergent sequences. 
 
 In this paper we compare these notions with their sequential versions in topological spaces. We will take the product spaces into account and give some results.