Treatise of Physics

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lemma A.505 A continuous partition of unity

open in the book · appendices/A-long-proofs.tex:24709 · p. 3039

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lemma A.505: A continuous partition of unityA.505definition 6.9: Compact set6.9definition 6.6: Continuous map6.6definition 6.24: Metric6.24lemma A.506: LocalityA.506proof : app:A-long-proofs@proof-300proofdefinition 6.5: Open cover6.5definition 7.142: Box-counting dimension7.142definition 7.127: Simple regions7.127definition A.498: Zero contentA.498definition A.529: Hausdorff; second countable; locally compactA.529definition 32.8: Attractor and basin32.8definition 12.41: The operator classes12.41definition 13.66: Smooth action; free; proper; orbit13.66lemma A.530: Two elementary facts about compactnessA.530lemma A.307: Partition of unity on a compact manifoldA.307lemma 13.136: Discrete subgroups of ℝ^f13.136proposition 6.10: Continuous images of compact sets6.10theorem A.550: Quoted: discrete subgroups of a real vector spaceA.550theorem A.244: Riesz–Markov; quotedA.244theorem A.242: Stone–Weierstrass; quotedA.242theorem 16.70: The direct method16.70theorem 32.42: The horseshoe is a full shift, quoted32.42theorem 32.30: Poincaré–Bendixson, restated from Part II32.30theorem 9.34: Poincaré–Bendixson; quoted9.34theorem 6.11: Heine–Borel on ℝ6.11theorem 6.12: Heine–Borel in ℝ^N6.12theorem 6.31: Compactness and sequential compactness6.31definition 3.53: Preimage3.53definition 6.2: Open set6.2definition 6.1: Topological space6.1definition A.361: Covering mapA.361definition 12.64: Strongly continuous one-parameter unitary group12.64definition 6.7: Homeomorphism6.7definition 6.15: Path-connected space6.15definition 6.17: Simply connected space6.17lemma A.531: The projection is openA.531proposition 6.28: \varepsilon–\delta characterization6.28definition 3.43: Map3.43definition 3.38: Ordered pair and Cartesian product3.38neighborhood truncated

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typedirectionnode provenancewhere
depends_on → Compact set declared appendices/A-long-proofs.tex:24717
depends_on → Continuous map declared appendices/A-long-proofs.tex:24717
depends_on → Metric declared appendices/A-long-proofs.tex:24717
depends_on ← Locality declared appendices/A-long-proofs.tex:24756
proves ← app:A-long-proofs@proof-300 declared appendices/A-long-proofs.tex:24720