Examples of 'isomorphisms' in a sentence
Meaning of "isomorphisms"
isomorphism (noun) - In mathematics, an isomorphism is a one-to-one correspondence between the elements of two sets that preserves the operations between the elements. This concept is also used in other fields like chemistry and computer science for structural equivalence
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- plural of isomorphism
How to use "isomorphisms" in a sentence
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isomorphisms
Isomorphisms between metric spaces are called isometries.
There are similar isomorphisms on symplectic manifolds.
Isomorphisms are formalized using category theory.
The uses of mathematical isomorphisms in general systems theory.
The transitions denoted by the arrows obey isomorphisms.
Order isomorphisms are functions that define such a renaming.
With respect to these generalized isomorphisms we develop a notion of independence.
The isomorphisms in this category are the diffeomorphisms defined above.
For a detailed discussion of relational homomorphisms and isomorphisms see.
The musical isomorphisms may also be extended to the bundles.
Logarithmic functions are the only continuous isomorphisms between these groups.
Isomorphisms preserve dimensions of subspaces.
Here the problem of the status of isomorphisms becomes fully relevant.
Isomorphisms between spaces of test functions and sequence spaces.
For all isomorphisms.
See also
It is important to note that there is a difference in the classifying isomorphisms used.
A topological obstruction prevents global isomorphisms between the sphere and the plane.
One of the important properties found in this embedding are the isomorphisms.
We show that this isomorphism is also an isomorphisms of the algebraic boundaries.
So the long exact cohomology sequences themselves ultimately separate into a chain of isomorphisms.
Are actually isomorphisms.
These two homomorphisms are clearly inverse to each other and thus are indeed isomorphisms.
The notion of recoupling requires a consistent choice of isomorphisms corresponding to regrouping of irreducible representations.
Three natural isomorphisms subject to certain coherence conditions expressing the fact that the tensor operation.
This follows from the fact that the composite of any two isomorphisms is an isomorphism.
Results on isomorphisms of Lie algebras of vector fields.
The cartesian morphisms of a fibre category FS are precisely the isomorphisms of FS.
These isomorphisms are the isomorphisms of Poincaré duality.
Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Isomorphisms of Groups.
Bijections are precisely the isomorphisms in the category Set of sets and set functions.
Through this construction, we have two mutually inverse isomorphisms.
Equality and Isomorphisms.
It is now sufficient to show that there are conjugations / natural isomorphisms.
In the category of sets, the isomorphisms are bijections.
Recursively, that would mean that there is an isomorphism between themes and isomorphisms.
In particular, they are both subject to isomorphisms which fix the lack of associativity.
The coherence theorem that we prove has the form " all diagrams of canonical isomorphisms commute ".
Sometimes the isomorphisms can seem obvious and compelling, but are still not equalities.
Big line bundles need not determine birational isomorphisms of X with its image.
The low-dimensional isomorphisms in the complex case have the following real forms.
In the category of topological spaces, morphisms are continuous functions and isomorphisms are called homeomorphisms.
Isomorphisms of G-sets are simply bijective equivariant maps.
In mathematical analysis, where the morphisms are differentiable functions, isomorphisms are also called diffeomorphisms.
Isomorphisms & other poems.
In the category of smooth manifolds, morphisms are smooth functions and isomorphisms are called diffeomorphisms.
In all cases, the isomorphisms are the “ obvious ” ones.
For a smooth CW complex X, there are natural isomorphisms.
Formally, bijections are precisely the isomorphisms in the category Set of sets and functions.
However, the term 'hylomorphism' does not apply solely to functions acting upon isomorphisms of lists.
