# Why are topological groups semitopological groups?

As part of a casual self-study of topology, I have started fooling around with topological groups. I noticed that the article on Wikipedia mentioned that "weakening the continuity conditions" gives the definition for a semitopological group as one in which the functions $l_g,r_g:G\rightarrow G$ defined by $l_g(h)=gh$ and $r_g(h)=hg$ are continuous for each group element $g$.

Since this is supposedly a weaker condition, every topological group should be semitopological, but I don't understand how one would go about proving this. I feel like I should be able to use some sort of relationship between continuous functions from $G\times G$ to $G$ and continuous functions from $G$ to $G$, but I haven't been able to find anything of that nature.

So how can it be proven that topological groups are semitopological?

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