Double cover
Encyclopedia
In mathematics
, a double cover or double covering may refer to:
Double coverage may also refer to:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a double cover or double covering may refer to:
- Double cover (topology), a two-to-one mapping from one topological space to another. Frequently occurring special cases include
- The orientable double cover of a non-orientable manifold.
- The bipartite double coverBipartite double coverIn graph theoretic mathematics, the bipartite double cover of an undirected graph G is a bipartite covering graph of G, with twice as many vertices as G. It can be constructed as the tensor product of graphs G × K2...
of an undirected graph G, formed by the graph tensor product G ×K2. - A double covering group of a topological group such as a Lie group, a group extensionGroup extensionIn mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence...
of index two formed by a topological double cover. A double cover may also be used to refer to non-topological group extensions of index two, for instance extensions of finite groups.
- Cycle double coverCycle double coverIn graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly twice...
, a collection of cycles in a graph that together include each edge twice. The cycle double cover conjecture is the unproven assertion that every bridgeless graph has a cycle double cover.
Double coverage may also refer to:
- Double coverageDouble coverageIn American and Canadian football double coverage is a state of defensive playcalling wherein two defensive players are assigned to "cover" one offensive player. This situation is often seen with standout wide receivers and running backs....
, a defensive strategy in American football, basketball, and other sports - Being covered by more than one health insuranceHealth insuranceHealth insurance is insurance against the risk of incurring medical expenses among individuals. By estimating the overall risk of health care expenses among a targeted group, an insurer can develop a routine finance structure, such as a monthly premium or payroll tax, to ensure that money is...
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