Cubical complex

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a cubical complex (also called cubical set and Cartesian complex) is a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> composed of <a href="/facts/Point_(geometry)/6YPAvX2a">points</a>, <a href="/facts/Line_segment/V8E0M4qk">line segments</a>, <a href="/facts/Square/JHJeMvmL">squares</a>, <a href="/facts/Cube/65lUaAqN">cubes</a>, and their <a href="/facts/Hypercube/q2mRPbIz"><i>n</i>-dimensional counterparts</a>. They are used analogously to <a href="/facts/Simplicial_complex/fF2282CF">simplicial complexes</a> and <a href="/facts/CW_complex/rN7buLMo">CW complexes</a> in the computation of the <a href="/facts/Homology_(mathematics)/VFJmryEW">homology</a> of <a href="/facts/Topological_space/v2ut7CbK">topological spaces</a>. <a href="/facts/CAT(k)_space/fmnJjYsN">Non-positively curved and CAT(0)</a> cube complexes appear with increasing significance in <a href="/facts/Geometric_group_theory/AJhxpFUe">geometric group theory</a>.
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Cubical complex open-in-new

Cubical complex