We show that the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the $\mathrm{PSL}_2(\mathbb{K})$ representation variety, where $\mathbb{K}=\mathbb{C}$ or $\mathbb{R}, answering a question of W. M. Goldman. We also prove the existence of faithful representations into $\mathrm{PU}(2,1)$ with certain nonintegral Toledo invariants.
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