How do you use Isomorphic in a sentence? See 10+ example sentences showing how this word appears in different contexts, including synonyms like isomorphous or similarity, plus the exact meaning.
Isomorphic in a sentence
Isomorphic meaning
- Related by an isomorphism; having a structure-preserving one-to-one correspondence.
- Having a similar structure or function to something that is not related genetically or through evolution.
- Having identical relevant structure; being structure-preserving while undergoing certain invertible transformations.
Synonyms of Isomorphic
Using Isomorphic
- The main meaning on this page is: Related by an isomorphism; having a structure-preserving one-to-one correspondence. | Having a similar structure or function to something that is not related genetically or through evolution. | Having identical relevant structure; being structure-preserving while undergoing certain invertible transformations.
- Useful related words include: isomorphous, similarity.
- In the example corpus, isomorphic often appears in combinations such as: isomorphic to, is isomorphic, are isomorphic.
Context around Isomorphic
- Average sentence length in these examples: 24.7 words
- Position in the sentence: 1 start, 13 middle, 6 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Isomorphic
- In this selection, "isomorphic" usually appears in the middle of the sentence. The average example has 24.7 words, and this corpus slice is mostly made up of statements.
- Around the word, space, necessarily, locally and mimicry stand out and add context to how "isomorphic" is used.
- Recognizable usage signals include 3 are isomorphic as lie and a minor isomorphic to the. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "isomorphic" sits close to words such as abstinence, adventurer and alters, which helps place it inside the broader word index.
Example types with isomorphic
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Any Dedekind-complete ordered field is isomorphic to the real numbers. (11 words)
It suggests two main sets of explanations for this: isomorphic mimicry and organisational overload. (14 words)
AmSi is a black solid isomorphic with LaSi, it has an orthorhombic crystal symmetry. (14 words)
An animation showing that the Petersen graph contains a minor isomorphic to the K 3,3 graph Klaus Wagner asked more generally whether any minor-closed class of graphs is determined by a finite set of " forbidden minors ". (38 words)
But two famous model-theoretic theorems deal with the weaker notion of κ-categoricity for a cardinal κ. A theory T is called κ-categorical if any two models of T that are of cardinality κ are isomorphic. (38 words)
Examples p-groups of the same order are not necessarily isomorphic ; for example, the cyclic group C 4 and the Klein four-group V 4 are both 2-groups of order 4, but they are not isomorphic. (37 words)
Example sentences (20)
A Banach space isomorphic to all its infinite-dimensional closed subspaces is isomorphic to a separable Hilbert space.
Examples p-groups of the same order are not necessarily isomorphic ; for example, the cyclic group C 4 and the Klein four-group V 4 are both 2-groups of order 4, but they are not isomorphic.
However, even though su(2) and so(3) are isomorphic as Lie algebras, SU(2) and SO(3) are not isomorphic as Lie groups.
It suggests two main sets of explanations for this: isomorphic mimicry and organisational overload.
A characterization of finite dimensionality is that a Hausdorff TVS is locally compact if and only if it is finite-dimensional (therefore isomorphic to some Euclidean space).
A contact analogue of the Darboux theorem holds: all contact structures on an odd-dimensional manifold are locally isomorphic and can be brought to a certain local normal form by a suitable choice of the coordinate system.
Actually, one can show that the subalgebra generated by any two elements of O is isomorphic to R, C, or H, all of which are associative.
Ado's theorem says every finite-dimensional Lie algebra is isomorphic to a matrix Lie algebra.
Algae In some multicellular green algae ( Ulva lactuca is one example), red algae and brown algae sporophytes and gametophytes may be externally indistinguishable (isomorphic).
AmSi is a black solid isomorphic with LaSi, it has an orthorhombic crystal symmetry.
An animation showing that the Petersen graph contains a minor isomorphic to the K 3,3 graph Klaus Wagner asked more generally whether any minor-closed class of graphs is determined by a finite set of " forbidden minors ".
An infinite-dimensional Banach space X is said to be homogeneous if it is isomorphic to all its infinite-dimensional closed subspaces.
Any Dedekind-complete ordered field is isomorphic to the real numbers.
Any group of prime order is isomorphic to a cyclic group and therefore abelian.
As an example, the automorphism group of (Z, +) contains only two elements, the identity transformation and multiplication with −1; it is isomorphic to Z/2Z.
As for classification, it can be shown that any connected Lie group with a given Lie algebra is isomorphic to the universal cover mod a discrete central subgroup.
A similar unsolved (as of 2011) question in free probability theory asks whether the von Neumann group algebras of any two non-abelian finitely generated free groups are isomorphic.
A surjective isometry between the normed vector spaces V and W is called an isometric isomorphism, and V and W are called isometrically isomorphic.
But if there are only finitely many summands, then the Banach space direct sum is isomorphic to the Hilbert space direct sum, although the norm will be different.
But two famous model-theoretic theorems deal with the weaker notion of κ-categoricity for a cardinal κ. A theory T is called κ-categorical if any two models of T that are of cardinality κ are isomorphic.
Common combinations with isomorphic
These word pairs occur most frequently in English texts:
- isomorphic to 71×
- is isomorphic 42×
- are isomorphic 14×
- naturally isomorphic 11×
- isomorphic if 6×
- be isomorphic 5×
- isomorphic as 4×
- isometrically isomorphic 4×
- not isomorphic 3×
- therefore isomorphic 3×