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[tuh-pol-uh-jee] /təˈpɒl ə dʒi/
noun, plural topologies for 3. Mathematics
the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching.
Also called point set topology. the study of limits in sets considered as collections of points.
a collection of open sets making a given set a topological space.
Origin of topology
1650-60; topo- + -logy
Related forms
[top-uh-loj-ik] /ˌtɒp əˈlɒdʒ ɪk/ (Show IPA),
topological, adjective
topologically, adverb
topologist, noun Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the web for topological
  • They were led into a topological trap and were not able to respond.
  • New evidence suggests fractal spiral pathways in microtubules supporting topological quantum computing.
  • There are many examples, and you can characterize them by topological invariants as well as by continuous parameters.
  • topological relationships describe relationships between objects in space.
  • A topological field is a topological vector space over each of its subfields.
  • Every topological vector space has a local base of absorbing and balanced sets.
  • A topological map is a very general type of map, the kind you might sketch on a napkin.
  • topological conjugation, which identifies equivalent dynamical systems.
British Dictionary definitions for topological


the branch of mathematics concerned with generalization of the concepts of continuity, limit, etc
a branch of geometry describing the properties of a figure that are unaffected by continuous distortion, such as stretching or knotting Former name analysis situs
(maths) a family of subsets of a given set S, such that S is a topological space
the arrangement and interlinking of computers in a computer network
the study of the topography of a given place, esp as far as it reflects its history
the anatomy of any specific bodily area, structure, or part
Derived Forms
topologic (ˌtɒpəˈlɒdʒɪk), topological, adjective
topologically, adverb
topologist, noun
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for topological



1610s (implied in topological), from topo-, comb. form of Greek topos "place" (see topos) + -logy.

Online Etymology Dictionary, © 2010 Douglas Harper
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topological in Science
The mathematical study of the geometric properties that are not normally affected by changes in the size or shape of geometric figures. In topology, a donut and a coffee cup with a handle are equivalent shapes, because each has a single hole.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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