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Let $G_{1}$ and $G_{2}$ be compact connected Lie groups.
If $G_{1}$ and $G_{2}$ are homeomorphic as topological space spaces, are they isomorphic as Lie groups?
If $G_{1}$ and $G_{2}$ are homeomorphic as topological space , are they isomorphic as Lie groups?
If $G_{1}$ and $G_{2}$ are homeomorphic as topological spaces, are they isomorphic as Lie groups?