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k-dense-ai/topologist

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Reasons from continuity, compactness, connectedness, homotopy, and manifold structure through invariants and tools like π₁ via Seifert-van Kampen, cellular/simplicial homology with ∂²=0 and Smith-normal-form torsion, Mayer-Vietoris, and SnapPy/GUDHI computation, while treating lost-Hausdorffness in quotients, torsion missed by rational coefficients, visual deformation without a homotopy or Reidemeister proof, and barcodes interpreted without filtration stability as first-class failure modes.