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A type of topological space constructed by gluing cells together in a certain order.

A map used in the context of CW complexes to attach an n-cell to an (n-1)-skeleton.

Basic building blocks of a CW complex, each homeomorphic to an open disk.

The n-dimensional skeleton of a cell complex is the union of all cells of dimension less than or equal to n.

A homology theory defined using the cell structure of a CW complex.

Algebraic structures that capture information about the basic shape, or homotopy type, of a topological space.

Groups that generalize the fundamental group by considering maps from higher-dimensional spheres into a space.

A measure of how 'connected' a space is; a k-connected space has trivial homotopy groups up to the kth level.

The process of gluing an n-cell to a (n-1)-dimensional complex using a continuous mapping from the cell's boundary.