Editing CW complex (section)

{{Short description|Type of topological space}}
In [[mathematics]], and specifically in [[topology]], a '''CW complex''' (also '''cellular complex''' or '''cell complex''') is a [[topological space]] that is built by gluing together topological balls (so-called ''cells'') of different dimensions in specific ways. It generalizes both [[topological manifold|manifolds]] and [[simplicial complex]]es and has particular significance for [[algebraic topology]].<ref>{{cite book|last=Hatcher|first=Allen|author-link=Allen Hatcher|title=Algebraic topology|publisher=[[Cambridge University Press]]|year=2002|isbn=0-521-79540-0}} This textbook defines CW complexes in the first chapter and uses them throughout; includes an appendix on the topology of CW complexes. A free electronic version is available on the [http://pi.math.cornell.edu/~hatcher/ author's homepage].</ref> It was initially introduced by [[J. H. C. Whitehead]] to meet the needs of [[homotopy theory]].<ref name=":2">{{cite journal|last=Whitehead|first=J. H. C.|author-link=J. H. C. Whitehead|year=1949a|title=Combinatorial homotopy. I.|url=https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-55/issue-3.P1/Combinatorial-homotopy-I/bams/1183513543.pdf|journal=[[Bulletin of the American Mathematical Society]]|volume=55|issue=5|pages=213&ndash;245|doi=10.1090/S0002-9904-1949-09175-9|mr=0030759|doi-access=free}} (open access)</ref>
CW complexes have better [[category theory|categorical]] properties than [[simplicial complex]]es, but still retain a combinatorial nature that allows for computation (often with a much smaller complex). 

The C in CW stands for "closure-finite", and the W for "weak" topology.<ref name=":2" />