Description: The unit group of a topological division ring is a topological group. (Contributed by Mario Carneiro, 5-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | istrg.1 | |- M = ( mulGrp ` R ) |
|
istdrg.1 | |- U = ( Unit ` R ) |
||
Assertion | tdrgunit | |- ( R e. TopDRing -> ( M |`s U ) e. TopGrp ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istrg.1 | |- M = ( mulGrp ` R ) |
|
2 | istdrg.1 | |- U = ( Unit ` R ) |
|
3 | 1 2 | istdrg | |- ( R e. TopDRing <-> ( R e. TopRing /\ R e. DivRing /\ ( M |`s U ) e. TopGrp ) ) |
4 | 3 | simp3bi | |- ( R e. TopDRing -> ( M |`s U ) e. TopGrp ) |