topology
Part of speech: noun
Morphological type: derivation
Topics: computing
engineering
geography
mathematics
medicine
natural-sciences
physical-sciences
sciences
technology
topography
topology
Etymology: From Late Latin topologia, from By surface analysis, topo- (“place”) + -logy (“study of, a branch of knowledge”).
Inflected forms:
form: topologies
pos: noun
tags: plural
Senses:
gloss: 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).
pos: noun
tags: uncountable
examples: 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.
gloss: 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.
pos: noun
tags: countable
uncountable
examples: A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).
The subsets of a set X which constitute a topology are called the open sets of X.
It is easy to verify that the topology generated by these basic open sets coincides with the definition of the topology on #92;widehat#123;V#125; above, for the Zariski topology and the sheaf of functions #92;operatorname#123;val#125;(f),f regular.
gloss: The anatomical structure of part of the body.
pos: noun
tags: countable
uncountable
gloss: The arrangement of nodes in a communications network.
pos: noun
tags: countable
uncountable
gloss: The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
pos: noun
tags: countable
uncountable
gloss: The topographical study of geographic locations or given places in relation to their history.
pos: noun
tags: countable
uncountable
gloss: The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.
pos: noun
tags: countable
dated
uncountable
Related words: topological
topologically
topological space
topologist
toponymy
homotopy
Derived words: Alexandrov topology
algebraic topology
bus topology
circuit 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
pointfree topology
pointless topology
point-set topology
pretopology
product topology
psychotopology
relative topology
retopology
ring topology
Scott topology
standard topology
star topology
subspace topology
subtopology
topologic
trivial topology
Zariski topology
Translations:
lang: Afrikaans
word: topologie
lang: Catalan
word: topologia
lang: Chinese Mandarin
word: 拓撲學 /拓扑学
roman: tuòpūxué
lang: Czech
word: topologie
lang: Danish
word: topologi
lang: Dutch
word: topologie
lang: Esperanto
word: topologio
lang: Estonian
word: topoloogia
lang: Finnish
word: topologia
lang: French
word: topologie
lang: Galician
word: topoloxía
lang: German
word: Topologie
lang: Greek
word: τοπολογία
roman: topología
lang: Hebrew
word: טופולוגיה
roman: topológya
lang: Hungarian
word: topológia
lang: Icelandic
word: grannfræði
lang: Icelandic
word: stöðfræði
lang: Irish
word: toipeolaíocht
lang: Italian
word: topologia
lang: Japanese
word: 位相幾何学
roman: isō-kikagaku
lang: Japanese
word: 位相数学
roman: isō-sūgaku
lang: Japanese
word: トポロジー
roman: toporojī
lang: Kazakh
word: топология
roman: topologiä
lang: Khmer
word: ឋានវិទ្យា
roman: thaanvityiə
lang: Korean
word: 위상수학
roman: wisangsuhak
lang: Latvian
word: topoloģija
lang: Macedonian
word: топологија
roman: topologija
lang: Malay
word: topologi
lang: Polish
word: topologia
lang: Portuguese
word: topologia
lang: Romanian
word: topologie
lang: Russian
word: тополо́гия
roman: topológija
lang: Serbo-Croatian
word: topologija
lang: Serbo-Croatian
word: топологија
lang: Sicilian
word: topoluggìa
lang: Slovene
word: topologija
lang: Spanish
word: topología
lang: Ukrainian
word: тополо́гія
roman: topolóhija
lang: Vietnamese
word: tô pô học