Treatise of Physics

Knowledge graph › Long Proofs

lemma A.531 The projection is open

open in the book · appendices/A-long-proofs.tex:25943 · p. 3052

Rests on

Supports

Neighborhood

Every logical edge within two steps of this node.

lemma A.531: The projection is openA.531definition 13.66: Smooth action; free; proper; orbit13.66definition 6.6: Continuous map6.6definition 6.2: Open set6.2lemma A.536: A slice is a chart domain downstairsA.536proposition A.532: Separation and countability of the quotientA.532proof : app:A-long-proofs@proof-319proofdefinition 13.48: Differentiable manifold13.48definition 13.49: Smooth map between manifolds13.49definition 6.9: Compact set6.9example 13.68: Why each hypothesis is there13.68lemma A.533: The orbit map has constant rank dA.533proposition A.535: Existence of a sliceA.535theorem 13.67: Quotient manifold theorem13.67definition 3.53: Preimage3.53definition 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.505: A continuous partition of unityA.505proposition 6.10: Continuous images of compact sets6.10proposition 6.28: \varepsilon–\delta characterization6.28definition A.141: MollificationA.141definition A.134: Mean-value propertyA.134definition A.529: Hausdorff; second countable; locally compactA.529definition 13.108: Star-shaped domain13.108definition 10.1: Partial differential equation; order10.1definition 6.3: Closed set6.3definition 6.13: Connected space6.13definition 6.4: Neighbourhood6.4definition 6.26: Open ball; metric topology6.26definition 6.5: Open cover6.5lemma A.365: Lebesgue numberA.365theorem A.537: The smooth structure on the orbit spaceA.537proof : app:A-long-proofs@proof-324prooflemma A.530: Two elementary facts about compactnessA.530remark A.542: Where each hypothesis is spentA.542proof : app:A-long-proofs@proof-320proof

Edges

typedirectionnode provenancewhere
depends_on → Smooth action; free; proper; orbit declared appendices/A-long-proofs.tex:25947
depends_on → Continuous map declared appendices/A-long-proofs.tex:25947
depends_on → Open set declared appendices/A-long-proofs.tex:25947
depends_on ← A slice is a chart domain downstairs declared appendices/A-long-proofs.tex:26180
depends_on ← Separation and countability of the quotient declared appendices/A-long-proofs.tex:25968
proves ← app:A-long-proofs@proof-319 declared appendices/A-long-proofs.tex:25951