In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.
Abstract
We characterize productively sequential spaces, that is, spaces whose product with every strongly sequential space is sequential, equivalently strongly sequential. It turns out that a regular topology is productively sequential if and only if it is sequential and bi-quasi-k.
Further aspects of I K-convergence in topological spaces
