Is an Archimedean topological group of the reals isomorphic to $(\mathbb R,+)$?

Question

A group $H:=(\mathbb R,\boxplus)$, is given to be

1. Ordered as per the canonical order of $\mathbb R$.
2. Archimedean as per order in 1.
3. Topological as per canonical topology of $\mathbb R$.

Can it be deduced that $H$ is group isomorphic to $(\mathbb R,+)$?

If not, what additional properties would be sufficient?

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I have found that, by a theorem of Hölder, any Archimedean group is group isomorphic to a subgroup of $(\mathbb R, +)$. Hence the question above reduces to whether, as a result of the fact that the set itself is $\mathbb R$ and $H$ topological, the case of $H$ being isomorphic to a proper subgroup of $(\mathbb R,+)$ can be excluded.