In mathematics, and specifically in topology, a CW complex (also cellular complex or cell complex) is a topological space that is built by gluing together...

contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable functor. More specifically...

smooth structure. Real projective space RPn admits the structure of a CW complex with 1 cell in every dimension. In homogeneous coordinates (x1 ... xn+1)...

extra constraints, such as being compactly generated weak Hausdorff or a CW complex. In the same vein as above, a "map" is a continuous function, possibly...

compression, and topological data analysis. Let X {\displaystyle X} be a CW complex and denote by X {\displaystyle {\mathcal {X}}} its set of cells. Define...

line with a single point removed. Real projective spaces have a simple CW complex structure, as Pn(R) can be obtained from Pn−1(R) by attaching an n-cell...

states that a map between CW-complexes can always be taken to be of a specific type. Concretely, if X and Y are CW-complexes, and f : X → Y is a continuous...

Every ANR has the homotopy type of a very simple topological space, a CW complex. Let X be a topological space and A a subspace of X. Then a continuous...

reduces a simplicial complex (or more generally, a CW complex) to a homotopy-equivalent subcomplex. Collapses, like CW complexes themselves, were invented...

decomposition for groups with more than one end. For a path connected CW-complex, the ends can be characterized as homotopy classes of proper maps R +...

{\displaystyle n} -cells. Each simplicial complex is a CW-complex, the inverse is not true. The construction of CW-complexes can be used to define cellular homology...

equivalence from a CW complex, this axiom reduces homology or cohomology theories on all spaces to the corresponding theory on CW complexes. Some examples...

Moreover, it is common to assume that this space is a CW-complex (which is always possible via CW approximation). The name is derived from Samuel Eilenberg...

Euclidean and CW complexes. Abstract cell complexes play an important role in image analysis and computer graphics. The idea of abstract cell complexes (also...

spaces. Algebraic topologists work with compactly generated spaces, CW complexes, or spectra. Formally, a homotopy between two continuous functions f...

the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy...

of the classifying space takes place within the homotopy category of CW complexes, existence theorems for universal bundles arise from Brown's representability...

finite CW-complexes. (When only triangular faces are used, they are two-dimensional finite simplicial complexes.) In general, for any finite CW-complex, the...

Look up CW in Wiktionary, the free dictionary. CW may stand for: centiwatt (cW), one hundredth of a watt Cω, a programming language CW complex, a type...

of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules. If X {\displaystyle X} is a CW-complex...

(1974): a spectrum (or CW-spectrum) is a sequence E := { E n } n ∈ N {\displaystyle E:=\{E_{n}\}_{n\in \mathbb {N} }} of CW complexes together with inclusions...

purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. A CW complex is a type of topological space introduced by J...

and is called the Bruschlinsky group. Provided X {\displaystyle X} is a CW-complex, it is isomorphic to the first cohomology group H 1 ( X ) {\displaystyle...

simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence...

n-skeleton of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices...

the following. 1. A finite 2-dimensional CW complex S R {\displaystyle S_{R}} , called the subdivision complex, with a fixed cell structure such that S...

the homotopy groups of the infinite symmetric product of a connected CW complex are the same as its reduced homology groups. The most common version of...

a CW-decomposition is to a topological space—in many regards the purpose of a handle decomposition is to have a language analogous to CW-complexes, but...

analytic varieties, semialgebraic sets, and subanalytic sets. CW-complexes A CW complex is a topological space formed by gluing disks of different dimensionality...

CW complexes in homotopy theory are generalized by analogous results for simplicial sets. While algebraic topologists largely continue to prefer CW complexes...