A Polish group is locally Roelcke precompact if there is a neighborhood of the identity element that is totally bounded in the Roelcke (or lower) group uniformity. These form a subclass of the locally bounded groups, while generalizing the Roelcke precompact and locally compact Polish groups.

We characterize these groups in terms of their geometric structure as those locally bounded groups whose coarsely bounded sets are all Roelcke precompact, and in terms of their uniform structure as those groups whose completions in the Roelcke uniformity are locally compact. We also assess the conditions under which this locally compact space carries the structure of a semi-topological semigroup.

如果单位元的邻域完全有界于 Roelcke（或更低）群一致性，则波兰群是局部 Roelcke 预紧的。它们形成了局部有界群的子类，同时概括了 Roelcke 预紧和局部紧波兰群。

我们根据几何结构将这些群刻画为粗有界集都是 Roelcke 预紧的局部有界群，而根据它们的均匀结构将这些群表征为在 Roelcke 均匀性中的完成是局部紧的群。我们还评估了这个局部紧凑空间承载半拓扑半群结构的条件。