Precompact set may refer to:

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Totally bounded space

bounded set is again totally bounded. The continuous image of a compact set is compact. The uniformly continuous image of a precompact set is precompact. Although

Compact space

Exhaustion by compact sets Lindelöf space Metacompact space Noetherian topological space Orthocompact space Paracompact space Precompact set - also called totally

Relatively compact subspace

mathematics, a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure is compact

Locally convex topological vector space

In a Hausdorff locally convex TVS, the convex hull of a precompact set is again precompact. Consequently, in a complete Hausdorff locally convex space

Polar topology

X'} has compact closure in the topology of uniform convergence on precompact sets. Furthermore, this topology on K {\displaystyle K} coincides with the

Approximation property

approximation property, if the identity map can be approximated, uniformly on precompact sets, by continuous linear maps of finite rank. For a locally convex space

Positive energy theorem

asymptotically Schwarzschild in the following sense: Suppose that K is an open precompact subset of M such that there is a diffeomorphism Φ : ℝ3 − B1(0) → M − K

Eberlein–Šmulian theorem

subsets are weakly precompact by Alaoglu's theorem. Thus the theorem implies that bounded subsets are weakly sequentially precompact, and therefore from