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A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

Cluster analysis is a technique used for classification of data in which data elements are partitioned into groups called clusters that represent collections of data elements ...

The Engel polyhedra are two 38-faced plesiohedra (and hence space-filling) discovered by Engel (Engel 1981; Engel 1986, p. 220; Grünbaum and Shephard 1980; Senechal 1990, ...

A functor is said to be faithful if it is injective on maps. This does not necessarily imply injectivity on objects. For example, the forgetful functor from the category of ...

Let P be a class of (universal) algebras. Then an algebra A is a local P-algebra provided that every finitely generated subalgebra F of A is a member of the class P. Note ...

A plesiohedron is the Voronoi cell of a so-called symmetric Delone set. Plesiohedra are space-filling polyhedra which have special symmetries that take any copy of the ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form M×V, where M is a four ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...