I would like to verify a certain condition for a theorem. It requires that $\{(\theta,\rho\theta):\rho>0,\theta>0\}$ has a non-empty interior. I have trouble visualizing such sets can you guys help me see if this has a non-empty interior (and if it does, why?)
2026-04-12 11:33:07.1775993587
Non-empty interior
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The set is the first quadrant with both axis removed which it is open, so in particular has a nonempty interior.