converges uniformly on Interaction with convexity The balanced hull of a totally bounded subset of a topological vector space is again totally bounded. The Minkowski sum of two compact (totally bounded) sets is compact (resp. totally bounded). In a locally convex (Hausdorff) space, the convex hull and the disked hull of a totally bounded set is totally bounded if and only if is complete. See also Compact space Locally compact space Measure of non-compactness Orthocompact space Paracompact space Relatively compact subspace References Bibliography Uniform spaces Metric geometry Topology Functional analysis Compactness (mathematics)