Linked from

The 59 pages that link to Compact space, each with the reason it gives.

• Extreme value theoremNarrower topic: Compactness supplies the key condition that keeps a function’s values from escaping their bounds.

• Bolzano–Weierstrass theoremNarrower topic: Compactness guarantees convergent subsequences in metric spaces, beyond Euclidean boundedness alone.

• Arzelà–Ascoli theoremNarrower topic: Compactness of the domain lets local continuity control be assembled across the whole space.

• Heine–Borel theoremNarrower topic: The theorem characterizes this general topological property using closedness and boundedness in Euclidean space.

• Compact operatorNarrower topic: Compact closure in the image is the defining destination property.

• Sequential compactnessNarrower topic: Compactness is the cover-based property often compared with sequential compactness.

• Banach–Alaoglu theoremNarrower topic: The theorem is a central compactness result for dual spaces.

• Prokhorov's theoremNarrower topic: Compactness of the closure is the topological outcome characterized by the theorem.

• Weierstrass theoremNarrower topic: Compactness is the domain condition that makes the theorem’s extrema attainable.

• Heine–Cantor theoremNarrower topic: Finite subcovers let local continuity neighborhoods yield a global uniform bound.

• Tube lemmaNarrower topic: A finite subcover lets local product neighborhoods combine into one neighborhood covering the compact factor.

• Eberlein–Šmulian theoremNarrower topic: Weak compactness is ordinary compactness applied to the weak topology.

• Buchdahl's theoremNarrower topic: The theorem is a sharp upper bound on stellar compactness under its assumptions.