leanprover-community / leanprover-community/mathlib4
Jordan Curve Theorem (JCT)
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Description
Zulip:
- #maths > Multivariate complex analysis
- #mathlib4 > Jordan curve / Smooth Jordan curve
- #PR reviews > Polygons PR
- #new members > Board Games in Lean @ 💬
- #mathlib4 > What will the Jordan Curve Theorem look like in mathlib?
- #triage > issue !4#35222: Jordan Curve Theorem (JCT)
There is a proof using HOL-Light (the main theorem is let JORDAN_CURVE_THEOREM), essentially proven by a limiting argument of the polygonal case, but we plan to use machinery from algebraic topology to prove the n-dimensional case in general spaces.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reading the linked HOL-Light proof in Jordan/jordan_curve_theorem.ml, especially the JORDAN_CURVE_THEOREM entry point, and review the linked Zulip discussions. The issue points toward algebraic-topology machinery for an n-dimensional result in general spaces, but does not identify Lean files or a concrete implementation boundary. Done would require a decided theorem shape and a completed mathlib formalization.
Written by the indexing model from the issue text.
Assessment
- Domain
- devtools
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 20/100