I studied that we do have a concept of total boundedness in a uniform space. I was thinking whether we have a concept of boundedness also in a uniform space (that need not be a metric space). Can anyone please tell?
2026-02-23 04:48:26.1771822106
Bounded uniform space
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Bourbaki's General Topology Ch.2 exercise 4.7: "A subset $A$ of a uniform space $X$ is said to be bounded if for each entourage $V$ of $X$ there is a finite set $F$ and an integer $n>0$ such that $A \subset V^n(F)$." Such definition I believe can be easily generalized to the entire space.