France Dacar

Jozef Stefan Institute
Ljubljana, Slovenia

Mathematical rambles

• The Cyclicity of a Hypergraph (PDF)
• Generative Structure of Entailment in Finite Constraint Networks (PDF)
• d'Alembert's Lemma (PDF)
  • d'Alembert's Lemma for Polynomials and The Fundamental Theorem of Algebra
  • d'Alembert's Lemma for Holomorphic Functions and The Maximum Modulus Theorem
• The join-induction principle for closure operators on dcpos (PDF)
• Bourbaki-Witt theorem
  • The proof of Bourbaki-Witt theorem in Lang's Algebra (PDF)
  • A cleaned-up version of the proof of Bourbaki-Witt theorem in Lang's Algebra (PDF)
  • Bourbaki-Witt theorem for dcpos is constructively equivalent to Bourbaki-Witt theorem for ccpos (PDF)
• A 'classical' proof that 2^(2^N) is homeomorphic to N (PDF)
• Oh, the fun I have with Paul J. Nahin's "When Least is Best"...
  • The Challenge Problem: Solved (PDF)
  • The Envelope-Folding Problem (PDF)
  • Some remarks (PDF)
• Farkas' lemma for cones (PDF)
• On Linear Independence of Characters (PDF)
• Quadratrix of Hippias and Viète's infinite product (PDF)
• An Infinite Sequence of Approximate Trisections (PDF)
• Approximate construction of a regular nonagon in Albrecht Dürer's "Painter's Manual" (PDF)
• The approximate regular nonagon in Wikipedia (PDF)
• Compactness of a Topological Space Via Subbase Covers (PDF)
• Characterizations of Compact Metric Spaces (PDF)
• All Triangular Squares (PDF)
• Fermat's two square theorem for rationals (PDF)
• The three squares theorem and enchanted walks (PDF)
• The kernel of a function from a module to a set (PDF)
• A triad of cubic curves associated with a triangle (PDF)