How to show that the usual metric with the usual addition is a topological group?
Can anybody please explain me briefly about topological groups and the way that I need to approach to this question?
How to show that the usual metric with the usual addition is a topological group?
Can anybody please explain me briefly about topological groups and the way that I need to approach to this question?
Let $n:\Bbb R\to\Bbb R:x\mapsto -x$ and $a:\Bbb R\times\Bbb R\to\Bbb R:\langle x,y\rangle\mapsto x+y$; $a$ is the operation of addition on $\Bbb R$, and $n$ is the operation of taking the additive inverse. To show that $\langle\Bbb R,+\rangle$ is a topological group when $\Bbb R$ is given the usual topology, you just have to show that the functions $n$ and $a$ are continuous. You don’t need to know anything more about topological groups; this is really just a beginning real analysis or metric topology problem stated in fancier language.