@MartinSleziak: I don't intend to keep this room alive anymore. Let it freeze.
user131753
Jun 13, 2019 13:15
@user2103480 I didn't claim that you don't know what an open set is. In any case, I don't think you understood the point I wanted to convey in my next-to-last comment to you. Let me try again. You wrote, "It's radius is the supremum of the radii of the open balls you took the union of." The point simply is that the supremum need not exist in $\mathbb{R}$.