(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this article, we define and study the concept of ideal topological groups. We study its relation to topological groups. We present examples that show that ideal topological groups and topological groups are independent concepts. We give a sufficient condition for a topological group to be an ideal topological group as well as we give a sufficient condition for an ideal topological group to be a topological group. Unlike topological groups, ideal topological groups are not nicely behaved with regard to subgroups. We give an example of a subgroup of an ideal topological group that is not an ideal topological group. We show that every open subgroup of an ideal topological group is also an ideal topological group. Moreover, we investigate I-connectedness of ideal topological groups.