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Topology

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...

There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. The only ...

Highly composite numbers are numbers such that divisor function d(n)=sigma_0(n) (i.e., the number of divisors of n) is greater than for any smaller n. Superabundant numbers ...

The Kneser graphs are a class of graph introduced by Lovász (1978) to prove Kneser's conjecture. Given two positive integers n and k, the Kneser graph K(n,k), often denoted ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...