Description: A normed group is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | ngptps | ⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ TopSp ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ngpms | ⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ MetSp ) | |
2 | mstps | ⊢ ( 𝐺 ∈ MetSp → 𝐺 ∈ TopSp ) | |
3 | 1 2 | syl | ⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ TopSp ) |