Non-empty interior 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?)

The set is the first quadrant with both axis removed which it is open, so in particular has a nonempty interior.