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...

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...

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)...

{\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...

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...

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

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...

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...

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...

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...

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...

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 +...

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

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...

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

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...

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...

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

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...

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

(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...

homotopy equivalence f : X → Y {\displaystyle f\colon X\to Y} of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion τ ( f )...

number n there is a contravariant functor Hn : C → Ab which assigns each CW-complex its nth cohomology group (with integer coefficients). Composing this with...

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

infinite symmetric product of a connected CW complex are the same as the reduced homology groups of that complex. That way, one can give a homotopical definition...

{\displaystyle \Gamma } is said to be of type Fn if there exists an aspherical CW-complex whose fundamental group is isomorphic to Γ {\displaystyle \Gamma } (a...