CW complex

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, and specifically in <a href="/facts/Topology/2EqW47cU">topology</a>, a CW complex (also cellular complex or cell complex) is a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> that is built by gluing together topological balls (so-called cells) of different dimensions in specific ways. It generalizes both <a href="/facts/Topological_manifold/eLKXMzzR">manifolds</a> and <a href="/facts/Simplicial_complex/fF2282CF">simplicial complexes</a> and has particular significance for <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a>. It was initially introduced by <a href="/facts/J._H._C._Whitehead/NhjAGNjR">J. H. C. Whitehead</a> to meet the needs of <a href="/facts/Homotopy_theory/MJwYyRny">homotopy theory</a>.
CW complexes have better <a href="/facts/Category_theory/6zS3DXPa">categorical</a> properties than <a href="/facts/Simplicial_complex/fF2282CF">simplicial complexes</a>, 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.

CW complex open-in-new

CW complex