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There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

A closed ideal I in a C^*-algebra A is called essential if I has nonzero intersection with every other nonzero closed ideal A or, equivalently, if aI={0} implies a=0 for all ...

A symbol used to represent the point and space groups (e.g., 2/m3^_). Some symbols have abbreviated form. The equivalence between Hermann-Mauguin symbols (a.k.a. ...

On the class of topological spaces, a homeomorphism class is an equivalence class under the relation of being homeomorphic. For example, the open interval (-pi/2,pi/2) and ...

For every infinite loop space machine E, there is a natural equivalence of spectra between EX and Segal's spectrum BX.

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

The equivalence of manifolds under continuous deformation within the embedding space. Knots of opposite chirality have ambient isotopy, but not regular isotopy.

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).

A functor which defines an equivalence of module categories.