topology
From Wiktionary, the free dictionary
Etymology
From Late Latin topologia, from Ancient Greek τόπος (tópos, “place, locality”) + -(o)logy (“study of, a branch of knowledge”).
Pronunciation
- (Received Pronunciation) IPA(key): /təˈpɒləd͡ʒi/
- (General American) IPA(key): /təˈpɑləd͡ʒi/
- Rhymes: -ɒlədʒi
Noun
topology (countable and uncountable, plural topologies)
- (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.
- 1970 [Addison-Wesley], Stephen Willard, General Topology, 2012, Dover, page v,
- (topology) Any collection τ 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 above, for the Zariski topology and the sheaf of functions regular.
- (medicine) The anatomical structure of part of the body.
- (computing) The arrangement of nodes in a communications network.
- (technology) The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
- (topography) The topographical study of geographic locations or given places in relation to their history.
- (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, π-system
Meronyms
Holonyms
Derived terms
- Alexandrov topology
- algebraic topology
- bus topology
- cofinite topology
- combinatorial topology
- differential topology
- discrete topology
- disjoint union topology
- ditopology
- electrotopology
- final topology
- geometric topology
- Grothendieck topology
- heterotopology
- hypertopology
- initial topology
- link topology
- mereotopology
- microtopology
- nanotopology
- network topology
- pointless topology
- point-set topology
- pretopology
- product topology
- psychotopology
- relative topology
- retopology
- ring topology
- Scott topology
- standard topology
- star topology
- subspace topology
- subtopology
- trivial topology
- Zariski topology
Related terms
Translations
study of geometric properties that are not changed by stretching etc.
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anatomical structure
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arrangements of computer nodes
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See also
Further reading
Anagrams
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