English

Products of CW complexes

General Topology 2018-08-31 v2 Algebraic Topology Logic

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.

Keywords

Cite

@article{arxiv.1710.05296,
  title  = {Products of CW complexes},
  author = {Andrew D. Brooke-Taylor},
  journal= {arXiv preprint arXiv:1710.05296},
  year   = {2018}
}

Comments

Expanded Introduction, rewrote Abstract, and fixed typos

R2 v1 2026-06-22T22:13:53.851Z