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full subgroup (Definition)

A subgroup of a topological group is full if it has a nonempty interior.

Theorem. A full subgroup is both open and closed.

Bibliography

1
Paul R. Halmos, Measure Theory, Springer-Verlag (1974).



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Other names:  open subgroup, clopen subgroup
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Cross-references: closed, open, interior, topological group, subgroup
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This is version 3 of full subgroup, born on 2007-05-12, modified 2007-06-11.
Object id is 9367, canonical name is FullSubgroup.
Accessed 854 times total.

Classification:
AMS MSC: 22A05 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Structure of general topological groups)
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