different between algebra vs topology

English

Etymology

From Medieval Latin algebr?ica, from Arabic word ????????? (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work ????????? ???????????? ??? ?????? ???????? ??????????????? (al-kit?b al-mu?ta?ar f? ?is?b al-jabr wa-l-muq?bala, “The Compendious Book on Calculation by Completion and Balancing”).

Pronunciation

• (UK) IPA^(key): /?æl.d??.b??/
• (US) IPA^(key): /?æl.d??.b??/, /?æl.d??.b??/

Noun

algebra (countable and uncountable, plural algebras)

1. (uncountable, mathematics) A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
2. (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
3. (uncountable, mathematics) The study of algebraic structures.
4. (countable, mathematics) A universal algebra.
5. (countable, algebra) An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.

   Synonyms: algebra over a field, algebra over a ring
6. (countable, set theory, mathematical analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).

   Synonyms: field of sets, algebra of sets

   Hypernym: ring

   Hyponym: ?-algebra

7. (countable, mathematics) One of several other types of mathematical structure.
8. (figuratively) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.

Derived terms

Related terms

Translations

Anagrams

• Labarge

Czech

Etymology

From Arabic ????????? (al-jabr, “reunion, resetting of broken parts”); see also the English algebra.

Pronunciation

• IPA^(key): [?al??bra]

Noun

algebra f

1. algebra

Declension

Derived terms

• Booleova algebra
• booleovská algebra

Related terms

• algebraický

Further reading

• algebra in P?íru?ní slovník jazyka ?eského, 1935–1957
• algebra in Slovník spisovného jazyka ?eského, 1960–1971, 1989

Danish

Etymology

Borrowed from Medieval Latin algebra, from Arabic ????????? (al-jabr).

Noun

algebra c (singular definite algebraen, not used in plural form)

1. (mathematics) algebra (using symbols)
2. (mathematics) algebra (study of algebraical structures)

Declension

Dutch

Etymology

From Middle Dutch algebra, from Latin algebra, from Arabic ????????? (al-jabr).

Pronunciation

• IPA^(key): /??l.???bra?/
• Hyphenation: al?ge?bra

Noun

algebra f (uncountable)

1. (mathematics) algebra

   Synonyms: stelkunde, stelkunst

Derived terms

• algebraïcus
• algebraïsch
• algebraïst
• lineaire algebra

Finnish

Noun

algebra

1. algebra

Declension

Hungarian

Etymology

From Latin algebra, from Arabic ????????? (al-jabr).

Pronunciation

• IPA^(key): [??l??br?]
• Hyphenation: al?geb?ra
• Rhymes: -r?

Noun

algebra

1. (mathematics) algebra (a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols)
2. (education) algebra (the study of algebra as a school subject)

Declension

Derived terms

• algebrai

References

Further reading

• algebra in Bárczi, Géza and László Országh: A magyar nyelv értelmez? szótára (’The Explanatory Dictionary of the Hungarian Language’). Budapest: Akadémiai Kiadó, 1959–1962. Fifth ed., 1992: ?ISBN
• algebra in Ittzés, Nóra (ed.). A magyar nyelv nagyszótára (’A Comprehensive Dictionary of the Hungarian Language’). Budapest: Akadémiai Kiadó, 2006–2031 (work in progress; published A–ez as of 2021)

Italian

Etymology

From Medieval Latin algebra, from Arabic ????????? (al-jabr, “reunion, resetting of broken parts”).

Pronunciation

• IPA^(key): /?al.d??e.bra/
• Hyphenation: al?ge?bra

Noun

algebra f (plural algebre)

1. algebra

Related terms

• algebrico
• algebrista

Anagrams

• alberga

Latin

Pronunciation

• (Classical) IPA^(key): /?al.?e.bra/, [?ä????b?ä]
• (Ecclesiastical) IPA^(key): /?al.d??e.bra/, [??l??d???b??]

Noun

algebra f (genitive algebrae); first declension

1. (Medieval Latin, New Latin) algebra

Declension

First-declension noun.

References

• algebra in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition, 1883–1887)

Latvian

Etymology

Via other European languages, ultimately from Medieval Latin algebra, from Arabic ????????? (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work ????????? ???????????? ??? ?????? ????????? ??????????????? (al-kit?b al-mu?ta?ar f? ?is?b al-jabr wa-l-muq?bala, “The Compendious Book on Calculation by Completion and Balancing”).

Pronunciation

• IPA^(key): [al??b?a]

Noun

algebra f (4th declension)

1. algebra is a branch of mathematics that studies generic numbers ('variables') regardless of their actual numeric value; the corresponding school subject

Declension

Derived terms

• algebrisks

Norwegian Bokmål

Etymology

From Arabic ????????? (al-jabr), via Medieval Latin algebra

Noun

algebra m (definite singular algebraen, indefinite plural algebraer, definite plural algebraene)

1. (mathematics) algebra
2. an algebra textbook

Derived terms

• algebraisk
• lineær algebra

References

• “algebra” in The Bokmål Dictionary.

Norwegian Nynorsk

Etymology

From Arabic ????????? (al-jabr), via Medieval Latin algebra

Noun

algebra m (definite singular algebraen, indefinite plural algebraer, definite plural algebraene)

1. (mathematics) algebra
2. an algebra textbook

Derived terms

• algebraisk
• lineær algebra

References

• “algebra” in The Nynorsk Dictionary.

Polish

Etymology

From Italian, Spanish or mediaeval Latin, from Arabic ????????? (al-jabr) “reunion”, “resetting of broken parts”, used in the title of al-Khwarizmi’s influential work ????????? ???????????? ??? ?????? ???????? ??????????????? (al-kit?b al-mu?ta?ar f? ?is?b al-jabr wa-l-muq?bala, “the compendious book on restoration and equating like with like”).

Pronunciation

• IPA^(key): /al???.bra/

Noun

algebra f

1. algebra

Declension

Derived terms

• algebraiczny
• algebraicznie
• algebraik

Further reading

• algebra in Polish dictionaries at PWN

Serbo-Croatian

Pronunciation

• IPA^(key): /?l?e?bra/
• Hyphenation: al?ge?bra

Noun

àlg?bra f (Cyrillic spelling ?????????)

1. algebra

Declension

Spanish

Noun

algebra

1. Misspelling of álgebra.

Swedish

Noun

algebra c

1. (mathematics) algebra

Declension

Related terms

• algebraisk
• relationsalgebra

English

Etymology

From Late Latin topologia, from Ancient Greek ????? (tópos, “place, locality”) + -(o)logy (“study of, a branch of knowledge”).

Pronunciation

• (Received Pronunciation) IPA^(key): /t??p?l?d?i/
• (General American) IPA^(key): /t??p?l?d?i/
• Rhymes: -?l?d?i

Noun

topology (countable and uncountable, plural topologies)

1. (mathematics, uncountable) The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).
   • 1970 [Addison-Wesley], Stephen Willard, General Topology, 2012, Dover, page v,

     This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields.

   • 1974 [Crane, Russak & Co.], H. Graham Flegg, From Geometry to Topology, 2001, Dover, page v,

     Many university courses in topology plunge immediately into a formalized and entirely abstract presentation of topological concepts.

2. (topology) Any collection ? of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.
   • 2016, Ehud Hrushovski, François Loeser, Non-Archimedean Tame Topology and Stably Dominated Types (AM-192), Princeton University Press, page 43,

     It is easy to verify that the topology generated by these basic open sets coincides with the definition of the topology on ${\displaystyle {\widehat {V}}}$ above, for the Zariski topology and the sheaf of functions ${\displaystyle \operatorname {val} (f),f}$ regular.

3. (medicine) The anatomical structure of part of the body.
4. (computing) The arrangement of nodes in a communications network.
5. (technology) The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
6. (topography) The topographical study of geographic locations or given places in relation to their history.
7. (dated) The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

Synonyms

• (branch of mathematics): analysis situs (obsolete), geometria situs (obsolete)

Hypernyms

• (collection of subsets): pi-system, ?-system

Meronyms

• open set

Holonyms

• topological space

Derived terms

Related terms

Translations

See also

• homotopy
• Appendix:Glossary of topology

Further reading

• topology on Wikipedia.Wikipedia
• Homotopy on Wikipedia.Wikipedia

Anagrams

• optology