feat: add Jordan–Brouwer separation eval problem#307
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§48 of Knill's "Some Fundamental Theorems in Mathematics" (Brouwer,
1912). High-dimensional generalization of the Jordan curve theorem:
for d ≥ 2, the complement in ℝᵈ of a topological (d-1)-sphere has
exactly two connected components. The hypothesis d ≥ 2 is essential
(in d = 1, the (d-1)-sphere is the two-point set {-1, 1} with three
complementary components). Mathlib has Metric.sphere, EuclideanSpace,
ConnectedComponents, Nat.card, but no Jordan–Brouwer separation
theorem, no Alexander duality, no invariance of domain in a form that
would discharge it. Stateable with zero new definitions.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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This PR adds an eval problem for the Jordan–Brouwer separation theorem
(L. E. J. Brouwer, 1912): the high-dimensional generalization of the
Jordan curve theorem. For
d ≥ 2, the complement inℝᵈof atopological
(d−1)-sphere has exactly two connected components.§48 of Knill's Some Fundamental Theorems in Mathematics.
The hypothesis
2 ≤ dis essential: in dimensiond = 1the(d−1)-sphere is the two-point set{−1, 1}, whose complement inℝhas three connected components.Mathlib has
Metric.sphere,EuclideanSpace,ConnectedComponents,Nat.card, but no Jordan–Brouwer separation theorem, no Alexanderduality, no invariance of domain in a form that would discharge it.
Stateable with zero new definitions.
No formalization found in any major prover.
🤖 Prepared with Claude Code