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A type of topological space that is constructed by iteratively attaching cells of increasing dimension.

An n-dimensional open disk whose boundary may be identified with other cells in a CW complex.

A sequence of subspaces $X^0 \subseteq X^1 \subseteq ... \subseteq X^n \subseteq ...$ where $X^n$ is the n-skeleton of a CW complex, containing cells of dimension at most $n$.

A continuous function between CW complexes that maps cells to cells while preserving dimensions.

A property of a CW complex wherein the closure of each cell intersects only finitely many other cells.

A homology theory for CW complexes that uses the skeletal structure of the complex to define chain complexes whose homology groups are easier to compute.

A homotopy theory concept where homotopy equivalences are defined in terms of deformation retractions in a cellular context.

A cell of dimension greater than or equal to two, representing a multi-dimensional aspect of a CW complex.

The topology of a CW complex where a subset is closed if its intersection with the closure of each cell is closed in the cell.

A result in homotopy theory stating that a weak homotopy equivalence between CW complexes induces isomorphisms on all homotopy groups.

A continuous function used to glue the boundary of an n-cell to a (n-1)-skeleton, formally defining the higher-dimensional cell attachments in a CW complex.

The subspace of a CW complex formed by cells of dimension $n$ or less, used in defining the complex structure and filtration.

A theorem that provides a bridge between homotopy and homology, stating that under certain conditions, the Hurewicz map from the fundamental group to the first homology group is an isomorphism.

A topological space obtained by identifying points in a larger space according to some equivalence relation; in the context of CW complexes, cells are attached to skeletons via quotient maps.