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isomorphism    音标拼音: [,ɑɪsəm'ɔrfɪzəm]
n. 同形,类质同像

同形,类质同像

isomorphism
n 1: (biology) similarity or identity of form or shape or
structure [synonym: {isomorphism}, {isomorphy}]

Isomorphism \I`so*mor"phism\, n. [Cf. F. isomorphisme.]
1. (Crystallog.) A similarity of crystalline form between
substances of similar composition, as between the
sulphates of barium ({BaSO4}) and strontium ({SrSO4}). It
is sometimes extended to include similarity of form
between substances of unlike composition, which is more
properly called {hom[oe]omorphism}.

2. (Math.) A one-to-one mapping of one set onto another set
which preserves the relations between the elements of the
domains of the sets.
[PJC]


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  • Isomorphism - Wikipedia
    An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as is the case for solutions of a universal property), or if the isomorphism is much more natural (in some sense) than other isomorphisms
  • 5. 6: Isomorphisms - Mathematics LibreTexts
    The following theorem illustrates a very useful idea for defining an isomorphism Basically, if you know what it does to a basis, then you can construct the isomorphism
  • Isomorphism | Group Theory, Algebraic Structures, Equivalence Relations . . .
    Isomorphism, in modern algebra, a one-to-one correspondence (mapping) between two sets that preserves binary relationships between elements of the sets For example, the set of natural numbers can be mapped onto the set of even natural numbers by multiplying each natural number by 2 The binary
  • Isomorphism — Definition, Formula Examples
    Isomorphism is a structure-preserving mapping between two mathematical objects that shows they are essentially the same in form, even if they look different Two objects are called isomorphic if such a mapping exists between them
  • Isomorphism -- from Wolfram MathWorld
    Isomorphism is a very general concept that appears in several areas of mathematics The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape " Formally, an isomorphism is bijective morphism Informally, an isomorphism is a map that preserves sets and relations among elements " is isomorphic to " is written Unfortunately, this symbol is also used to
  • ISOMORPHISM Definition Meaning - Merriam-Webster
    The meaning of ISOMORPHISM is the quality or state of being isomorphic
  • Isomorphism theorems - Wikipedia
    Isomorphism theorems In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and other algebraic
  • ISOMORPHISM Definition Meaning | Dictionary. com
    ISOMORPHISM definition: the state or property of being isomorphous or isomorphic See examples of isomorphism used in a sentence
  • Group Isomorphism: Definition, Properties, Examples - Mathstoon
    Group Isomorphism: Definition, Properties, Examples An isomorphism of groups is a special kind of group homomorphisms It preserves every structure of groups In this article, we will learn about isomorphism between groups, related theorems, and applications
  • 5. 6: Isomorphisms - Mathematics LibreTexts
    In this section we will consider linear transformations that are one to one and onto nbsp; Such linear transformations are called isomorphisms





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