Products of CW complexes
Abstract
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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