topology
Language: English
Part of speech: noun
Pronunciation: ipa: /təˈpɒləd͡ʒi/
ipa: /təˈpɑləd͡ʒi/
rhymes: -ɒlədʒi
Forms: form: topologies
Etymology: From Late Latin topologia, from Ancient Greek τόπος (tópos, “place, locality”) + -(o)logy (“study of, a branch of knowledge”).
Senses: 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.
topics: mathematics
sciences
glosses: 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).
examples: text: A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).
text: The subsets of a set X which constitute a topology are called the open sets of X.
text: 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.
ref: 2016, Ehud Hrushovski, François Loeser, Non-Archimedean Tame Topology and Stably Dominated Types (AM-192), Princeton University Press, page 43:
topics: mathematics
sciences
topology
glosses: 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.
topics: medicine
sciences
glosses: The anatomical structure of part of the body.
topics: computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: The arrangement of nodes in a communications network.
topics: engineering
natural-sciences
physical-sciences
technology
glosses: The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
topics: geography
natural-sciences
topography
glosses: The topographical study of geographic locations or given places in relation to their history.
glosses: The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.
Synonyms: sense: branch of mathematics
word: analysis situs
sense: branch of mathematics
word: geometria situs
Hypernyms: sense: collection of subsets
word: pi-system
sense: collection of subsets
word: π-system
Meronyms: open set
Derived terms: 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
trivial topology
Zariski topology
Related terms: topological
topologically
topological space
topologist
toponymy
homotopy