Abstract
In this article, we define a new cardinal function called the closure index of a semitopological group. The closure index ci(G) of a semitopological group G satisfying the T1-separation axiom lies between their character and pseudocharacter. For locally compact topological groups, these three cardinal functions coincide. We extend this result to the class of feathered topological groups and determine the value of the closure index for other classes of topological groups with compact-like properties. We also present several examples of topological groups with compact-like properties for which the three cardinal functions are pairwise distinct.We also find some classes of topological groups of countable pseudocharacter that have countable closure index.
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