CW complexes

A CW complex is a way mathematicians build and study complex shapes by gluing together simple parts called cells—points, lines, disks, and higher-dimensional analogs. These cells are added step-by-step in a structured way: starting with points, then attaching lines, then disks, and so on, forming a layered, flexible model of the shape’s structure. This approach simplifies understanding the shape’s properties, like holes or connectedness, by breaking it down into manageable, well-organized pieces. CW complexes are fundamental in topology because they provide a systematic way to analyze and classify complicated spaces.