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arxiv: 1710.05296 · v2 · pith:WK53XU2Fnew · submitted 2017-10-15 · 🧮 math.GN · math.AT· math.LO

Products of CW complexes

Andrew D. Brooke-Taylor This is my paper
classification 🧮 math.GN math.ATmath.LO
keywords complexescomplexproductaxiomsextraset-theoreticalgebraiccharacterization
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CW complexes are used extensively in algebraic topology, but the product of two CW complexes need not be a CW complex, as shown by Dowker. Whilst Whitehead and Milnor gave sufficient conditions for the product to be a CW complex, all existing characterizations of those pairs of CW complexes which have product a CW complex rely on extra set-theoretic axioms. Here we provide a complete characterization of when the product of two CW complexes is a CW complex without using any extra set-theoretic axioms.

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  1. Short, new proofs of Dowker duality

    math.AT 2024-08 unverdicted novelty 6.0

    Three new proofs of Dowker duality are presented using poset fiber lemmas, along with a generalization showing that homologies of simplicial complexes and relational complexes form a long exact sequence.