CW complex

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 manifolds and simplicial complexes and has particular significance for algebraic topology.^[1] It was initially introduced by J. H. C. Whitehead to meet the needs of homotopy theory.^[2] CW complexes have better categorical properties than simplicial complexes, 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.^[2]

^ Hatcher, Allen (2002). Algebraic topology. Cambridge University Press. 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 author's homepage.
^ ^a ^b Whitehead, J. H. C. (1949a). "Combinatorial homotopy. I." (PDF). Bulletin of the American Mathematical Society. 55 (5): 213–245. doi:10.1090/S0002-9904-1949-09175-9. MR 0030759. (open access)

[1] Hatcher, Allen (2002). Algebraic topology. Cambridge University Press. 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 author's homepage.

[:2-2] Whitehead, J. H. C. (1949a). "Combinatorial homotopy. I." (PDF). Bulletin of the American Mathematical Society. 55 (5): 213–245. doi:10.1090/S0002-9904-1949-09175-9. MR 0030759. (open access)

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