leanprover-community / leanprover-community/mathlib4

Prove that inversion is discontinuous at the center

Open
#5,939 4 comments 0 reactions 0 assignees View on GitHub

Nobody has claimed this yet.

good first issue t-analysis t-euclidean-geometry t-topology
Dominant language
Lean
Stars
4.2k
Forks
1.7k
No merged PRs in 30d

Description

  • Prove Tendsto (inversion c R) (𝓝[≠] c) cobounded if R ≠ 0.
  • Deduce that inversion c R is discontinuous at c if R ≠ 0
    and the vector space is nontrivial.
  • Deduce that fderiv (inversion c R) c is zero, thus
    fderiv (inversion c R) x = ((R / dist x c) ^ 2 • (reflection (ℝ ∙ (x - c))ᗮ : F →L[ℝ] F)) x
    for all x (see #5937 for the case x ≠ c).

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Read the three unchecked goals in the issue and compare the x ≠ c case in #5937; then identify the existing inversion and fderiv results they build on. Done means all three statements are proved, including discontinuity in a nontrivial vector space and the stated derivative formula.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
4/5
Estimated time
3-5 days
Activity status
Quiet
Clarity
Mostly clear
Newbie friendliness
45/100

Get new issues in your inbox

A short digest of beginner-friendly GitHub issues.