Definitions for mathematical structure
math·e·mat·i·cal struc·ture

WiktionaryRate this definition:3.0 / 1 vote

1. mathematical structurenoun

   A set together with a collection of mathematical objects such as other sets, relations or operations which endow it with additional stucture.

WikipediaRate this definition:0.0 / 0 votes

1. Mathematical structure

   In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories. Sometimes, a set is endowed with more than one feature simultaneously, which allows mathematicians to study the interaction between the different structures more richly. For example, an ordering imposes a rigid form, shape, or topology on the set, and if a set has both a topology feature and a group feature, such that these two features are related in a certain way, then the structure becomes a topological group.Mappings between sets which preserve structures (i.e., structures in the domain are mapped to equivalent structures in the codomain) are of special interest in many fields of mathematics. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures.

WikidataRate this definition:4.5 / 2 votes

1. Mathematical structure

   In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance. A partial list of possible structures are measures, algebraic structures, topologies, metric structures, orders, equivalence relations, differential structures, and categories. Sometimes, a set is endowed with more than one structure simultaneously; this enables mathematicians to study it more richly. For example, an order induces a topology. As another example, if a set both has a topology and is a group, and the two structures are related in a certain way, the set becomes a topological group. Mappings between sets which preserve structures are of special interest in many fields of mathematics. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures. N. Bourbaki suggested an explication of the concept "mathematical structure" in their book "Theory of Sets" and then defined on that base, in particular, a very general concept of isomorphism.

How to pronounce mathematical structure?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

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   Fred

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   Tessa

   South African

How to say mathematical structure in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of mathematical structure in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of mathematical structure in Pythagorean Numerology is: 8

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Mathematical_Structure
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Mathematical_Structure
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=mathematical structure