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...

{\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...

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...

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

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...

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...

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...

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

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...

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 +...

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

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...

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...

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...

{\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...

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...

structure of a CW-complex, one may consider the category of principal G-bundles. One can define a functor from the category of CW-complexes to the category...

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 )...

sets Chain complex, an algebraic structure Simplicial complex, a kind of topological space CW complex, a kind of topological space Line complex, a 3-dimensional...

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

(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...

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