Topological automorphism-invariant subgroup
This article defines a property that can be evaluated for a subgroup of a semitopological group
ANALOGY: This is an analogue in topological group of a property encountered in group. Specifically, it is a topological subgroup property analogous to the subgroup property: characteristic subgroup
View other analogues of characteristic subgroup | View other analogues in topological groups of subgroup properties (OR, View as a tabulated list)
Definition with symbols
A subgroup of a topological group is said to be topological automorphism-invariant or topologically characteristic in if given a topological automorphism ( is thus both a homeomorphism and an automorphism), .
Any topological subgroup-defining function on topological groups, must always output a topologically characteristic subgroup.