Products of CW complexes
Andrew D. Brooke-Taylor
TL;DR
This paper provides a complete characterization of when the product of two CW complexes is itself a CW complex, eliminating the need for additional set-theoretic assumptions, which advances understanding in algebraic topology.
Contribution
It offers a new characterization of CW complex products that does not depend on extra set-theoretic axioms, unlike previous results.
Findings
Characterization of CW complex products without extra axioms
Conditions under which product of CW complexes is a CW complex
Advancement in algebraic topology understanding
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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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Computability, Logic, AI Algorithms