Open subgroup: Difference between revisions
m (1 revision) |
No edit summary |
||
| Line 1: | Line 1: | ||
{{ | {{semitopological subgroup property}} | ||
==Definition== | ==Definition== | ||
A [[subgroup]] of a [[ | A [[subgroup]] of a [[semitopological group]] is termed an '''open subgroup''' if it is an [[tps:open subset|open subset]] in the [[tps:subspace topology|subspace topology]]. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Latest revision as of 22:15, 14 January 2012
This article defines a property that can be evaluated for a subgroup of a semitopological group
Definition
A subgroup of a semitopological group is termed an open subgroup if it is an open subset in the subspace topology.
Relation with other properties
Stronger properties
Weaker properties
Facts
- All cosets of an open subgroup are open. Thus, in a connected topological group, there cannot exist any proper open subgroup.
- In a compact group, any open subgroup must have finite index