View example sentences, synonyms and word forms for Isomorphism.
Isomorphism meaning
Similarity of form | Similarity of form | the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.
Synonyms of Isomorphism
Isomorphism vertaling naar Nederlands
Example sentences (20)
Another typical example is the statement that "there are two different groups of order 4 up to isomorphism ", or "modulo isomorphism, there are two groups of order 4".
Conversely, a particular map between particular objects may be called an unnatural isomorphism (or "this isomorphism is not natural") if the map cannot be extended to a natural transformation on the entire category.
Given an object X, a functor G (taking for simplicity the first functor to be the identity) and an isomorphism proof of unnaturality is most easily shown by giving an automorphism that does not commute with this isomorphism (so ).
On this view and in this sense, these two sets are not equal because one cannot consider them identical: one can choose an isomorphism between them, but that is a weaker claim than identity—and valid only in the context of the chosen isomorphism.
This leads to a third notion, that of a natural isomorphism : while V and V** are different sets, there is a "natural" choice of isomorphism between them.
A bijective map between two totally ordered sets that respects the two orders is an isomorphism in this category.
A groupoid is a category in which every morphism is an isomorphism.
Also called an endomorphism of G. ; Automorphism : An endomorphism that is bijective, and hence an isomorphism.
An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate.
Another way to express this is that any vector space is completely classified ( up to isomorphism) by its dimension, a single number.
Any bijective ring homomorphism is a ring isomorphism.
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus.
A ring homomorphism between the same ring is called an endomorphism and an isomorphism between the same ring an automorphism.
A ring homomorphism is said to be an isomorphism if there exists an inverse homomorphism to f (i.
As is the case for Galois groups, the real interest lies often in refining a correspondence to a duality (i.e. antitone order isomorphism).
A surjective isometry between the normed vector spaces V and W is called an isometric isomorphism, and V and W are called isometrically isomorphic.
A theory is called categorical if it determines a structure up to isomorphism, but it turns out that this definition is not useful, due to serious restrictions in the expressivity of first-order logic.
Because is an isomorphism, it translates multiplication of positive real numbers into addition of real numbers.
Bicategories are a weaker notion of 2-dimensional categories in which the composition of morphisms is not strictly associative, but only associative "up to" an isomorphism.
But there is in general no natural isomorphism between these two spaces.