Mathematics — Graph Theory · contractible-cw-complexes
Problem
Show that a CW complex is contractible if it is the union of an increasing sequence of subcomplexes X1⊂X2⊂⋯ such that each inclusion Xi↪Xi+1 is nullhomotopic, a condition sometimes expressed by saying Xi is contractible in Xi+1. An example is S∞, or more generally the infinite suspension S∞X of any CW complex X, the union of the iterated suspensions SnX.