topology en · NOUN
Pronunciation
- /təˈpɑləd͡ʒi/ (General-American)
- /təˈpɒləd͡ʒi/ (Received-Pronunciation)
- (US) audio
Etymology
From Late Latin topologia, from By surface analysis, topo- (“place”) + -logy (“study of, a branch of knowledge”).
Meanings
-
(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).
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, 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.
-
(countable, uncountable) 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.
A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).
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.
2016, Ehud Hrushovski, François Loeser, Non-Archimedean Tame Topology and Stably Dominated Types (AM-192), Princeton University Press, page 43:The subsets of a set X which constitute a topology are called the open sets of X.
- (countable, uncountable) The anatomical structure of part of the body.
- (countable, uncountable) The arrangement of nodes in a communications network.
- (countable, uncountable) The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
- (countable, uncountable) The topographical study of geographic locations or given places in relation to their history.
- (countable, dated, uncountable) The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| topologies | Number=Plur | lexicographic |
Deriveds
combinatorial topology · differential topology · final topology · link topology · Alexandrov topology · cofinite topology · pointless topology · mereotopology · disjoint union topology · point-set topology · subtopology · discrete topology · hypertopology · Scott topology · retopology · initial topology · psychotopology · Zariski topology · star topology · Grothendieck topology · algebraic topology · network topology · subspace topology · ring topology · heterotopology · topologic · ditopology · circuit topology · trivial topology · relative topology · microtopology · pretopology · bus topology · product topology · standard topology · pointfree topology · electrotopology · nanotopology · geometric topology
Holonyms
Hypernyms
pi-system (collection of subsets) · π-system (collection of subsets)
Meronyms
Relateds
topologist · toponymy · homotopy · topological · topological space · topologically
Synonyms
analysis situs (branch of mathematics) · geometria situs (branch of mathematics)
Translations (59)
hu topológia (study of geometric properties that are not changed by stretching etc.) · fr topologie (study of geometric properties that are not changed by stretching etc.) · id topologi (arrangements of computer nodes) · fi topologia (arrangements of computer nodes) · sh topologija (arrangements of computer nodes) · ja トポロジー (study of geometric properties that are not changed by stretching etc.) · el τοπολογία (arrangements of computer nodes) · ja 位相幾何学 (study of geometric properties that are not changed by stretching etc.) · af topologie (study of geometric properties that are not changed by stretching etc.) · cmn 拓撲學 /拓扑学 (study of geometric properties that are not changed by stretching etc.) · lv topoloģija (study of geometric properties that are not changed by stretching etc.) · pt topologia (arrangements of computer nodes) · fa-ira توپولوژی (study of geometric properties that are not changed by stretching etc.) · el τοπολογία (study of geometric properties that are not changed by stretching etc.) · et topoloogia (study of geometric properties that are not changed by stretching etc.) · ro topologie (study of geometric properties that are not changed by stretching etc.) · sh topologija (study of geometric properties that are not changed by stretching etc.) · ja トポロジー (arrangements of computer nodes) · vi tô pô học (study of geometric properties that are not changed by stretching etc.) · he טופולוגיה (study of geometric properties that are not changed by stretching etc.) · eo topologio (study of geometric properties that are not changed by stretching etc.) · scn topoluggìa (study of geometric properties that are not changed by stretching etc.) · ga toipeolaíocht (study of geometric properties that are not changed by stretching etc.) · ms topologi (study of geometric properties that are not changed by stretching etc.) · mi āhuawhatunga (arrangements of computer nodes) · gl topoloxía (study of geometric properties that are not changed by stretching etc.) · sh topologija (anatomical structure) · ru тополо́гия (arrangements of computer nodes) · es topología (study of geometric properties that are not changed by stretching etc.) · hu topológia (arrangements of computer nodes) · ru тополо́гия (study of geometric properties that are not changed by stretching etc.) · cmn 拓撲 /拓扑 (arrangements of computer nodes) · ko 위상수학 (study of geometric properties that are not changed by stretching etc.) · ja 位相数学 (study of geometric properties that are not changed by stretching etc.) · da topologi (study of geometric properties that are not changed by stretching etc.) · pt topologia (study of geometric properties that are not changed by stretching etc.) · cs topologie (arrangements of computer nodes) · nl topologie (study of geometric properties that are not changed by stretching etc.) · de Topologie (study of geometric properties that are not changed by stretching etc.) · is stöðfræði (study of geometric properties that are not changed by stretching etc.) · sl topologija (study of geometric properties that are not changed by stretching etc.) · it topologia (study of geometric properties that are not changed by stretching etc.) · pl topologia (study of geometric properties that are not changed by stretching etc.) · km ឋានវិទ្យា (study of geometric properties that are not changed by stretching etc.) · de Topologie (arrangements of computer nodes) · sh топологија (study of geometric properties that are not changed by stretching etc.) · cs topologie (study of geometric properties that are not changed by stretching etc.) · is grannfræði (study of geometric properties that are not changed by stretching etc.) · uk тополо́гія (study of geometric properties that are not changed by stretching etc.) · fi topologia (study of geometric properties that are not changed by stretching etc.) · ar طوبولوجيا (study of geometric properties that are not changed by stretching etc.) · sh топологија (anatomical structure) · fr topologie (arrangements of computer nodes) · ca topologia (study of geometric properties that are not changed by stretching etc.) · mk топологија (study of geometric properties that are not changed by stretching etc.) · el τοπολογία (anatomical structure) · kk топология (study of geometric properties that are not changed by stretching etc.) · ru тополо́гия (anatomical structure) · sh топологија (arrangements of computer nodes)