Construction of Spaces: Cell Complexes and more Adjunction Spaces

(21.1) We consider now a special class of spherical complexes called finite cell complexes. These are compact Hausdorff spaces Z such that Z has a finite collection of closed subsets c j q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502408/295d3acc-dfa3-4421-a2d3-a9c22ffb681c/content/eq610.tif"/> (were q = 0, 1, …, represents the dimension, and j ranges over some index set J_q ) with the following properties: Let Z q = ∪ { c j p |   all  j ∈ J p ,     all     p ≤ q } , Z − 1 = empty     set , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502408/295d3acc-dfa3-4421-a2d3-a9c22ffb681c/content/eq611.tif"/>