I'm currently studying uniform spaces and have come across a problem I don't know how to solve. Given any vicinity $U$ of a non-discrete uniform space, I want to prove that for every pair of points $a, b$ there is a $n\in\mathbb{N}$ such that $(a, b) \in \underbrace{U \circ U \circ U ... \circ U}_\textrm{n compositions}$. I've spent a few days thinking about the problem and haven't gotten anywhere. I fear this should be really obvious, and the fact that I'm not able to prove it means there is something wrong with my way of reasoning with uniformities. Could anyone point me in the direction of a proof?
2026-02-23 04:44:19.1771821859
Bounded Point in Uniform Spaces
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