They can all be represented in an essentially unique way as Seifert fiber spaces : the quotient manifold is a sphere and there are 3 exceptional fibers of orders 2, 3, and 3.
22.
They can all be represented in an essentially unique way as Seifert fiber spaces : the quotient manifold is a sphere and there are 3 exceptional fibers of orders 2, 3, and 4.
23.
They can all be represented in an essentially unique way as Seifert fiber spaces : the quotient manifold is a sphere and there are 3 exceptional fibers of orders 2, 3, and 5.
24.
One alternative proposal that has been developed is the theory of derivators that "-category is canonically triangulated, and moreover mapping cones become essentially unique ( in a precise homotopical sense ).
25.
A related notion is a universal property, where an object is not only essentially unique, but unique " up to a unique isomorphism " ( meaning that it has trivial automorphism group ).
26.
On the other hand, there is not an essentially unique group with exactly 4 elements, as there are two non-isomorphic examples : the cyclic group of order 4 and the Klein four group.
27.
The Caballo Mountains are essentially unique in New Mexico because their section of exposed rocks begins in Precambrian time, and runs through every geological period of the Phanerozoic eon with the exceptions of the Triassic and Jurassic.
28.
Every closed 3-manifold has a prime decomposition : this means it is the connected sum of prime 3-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).
29.
Every Boolean algebra " A " has an essentially unique completion, which is a complete Boolean algebra containing " A " such that every element is the supremum of some subset of " A ".
30.
If the space " X " has a universal cover then that universal cover is essentially unique : if the mappings and are two universal covers of the space " X " then there exists a homeomorphism such that.
