Conjectures about the Mandelbrot and Multibrot sets
A stronger version of the MLC conjecture, stating that all multibrots are locally connected. Note that we don't need to require 2 ≤ n because the conjecture holds in the trivial cases n = 0 and n = 1 too.
Mathematical statement
A stronger version of the MLC conjecture, stating that all multibrots are locally connected.
Note that we don't need to require 2 ≤ n because the conjecture holds in the trivial cases n = 0
and n = 1 too.
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
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Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
MLC_general_exponent
theorem MLC_general_exponent (n : ℕ) : LocallyConnectedSpace (multibrotSet n) := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References