メモ
https://ncatlab.org/nlab/show/CW+complex
nLab
CW complex
1. Idea
2. Definition
3. Properties
Closure properties
Local contractibility
Compactness properties
Up to homotopy equivalence
Subcomplexes
Fibrations
Singular homology
4. Examples
5. Related concepts
(抜粋)
Remark 1.1. (origin of the “CW” terminology)
Thus the CW’ stands for the following two properties shared by any CW complex:
・C = “closure finiteness”: a compact subset of a CW complex intersects the interior of only finitely many cells (prop.), hence in particular so does the closure of any cell.
・W = “weak topology”: Since a CW-complex is a colimit in Top over its cells, and as such equipped with the final topology of the cell inclusion maps, a subset of a CW-complex is open or closed precisely if its restriction to (the closure of) each cell is open or closed, respectively.
(Whitehead called the interior of the n-disks the “cells”, so that their closure of each cell is the corresponding n-disk.)
(引用終り)