Why is topology defined?

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[ tuh-pol-uh-jee ]SHOW IPA

/ təˈpɒl ə dʒi /PHONETIC RESPELLING

Middle School Level

This shows grade level based on the word's complexity.

noun, plural to·pol·o·gies 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 to·pol·o·gy . the study of limits in sets considered as collections of points.

a collection of open sets making a given set a topological space.

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Rarely a·nal·y·sis si·tus[uh-nal uh sis sahy tuhs, see-] /əˈnæl ə sɪs ˈsaɪ təs, ˈsi-/ [for defs. 1, 2] .

Origin of topology

First recorded in 165060; topo- + -logy

OTHER WORDS FROM topology

top·o·log·ic[top-uh-loj-ik], /ˌtɒp əˈlɒdʒ ɪk/, top·o·log·i·cal, adjectivetop·o·log·i·cal·ly, adverbto·pol·o·gist, noun

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2021

How to use topology in a sentence

  • It is called topological because its understanding and analysis requires topology, the branch of pure math that studies how shapes change when stretched, bent or twisted.

  • Alexander won first place in the mathematics category at this years International Science and Engineering Fair, and has long had an interest in topology which just might have been related to the puzzle.

  • Alexander won first place in the mathematics category at this years International Science and Engineering Fair for his work at the intersection of topology and medicine.

  • Alexander has long had an interest in topology, which just might be related to his submitted puzzle.

  • At first, topology can seem like an unusually imprecise branch of mathematics.

  • Fade is a function of geography and topology, the graybeard said quietly.

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British Dictionary definitions for topology

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 knottingFormer 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 of topology

topologic [ˌtɒpəˈlɒdʒɪk] or topological, adjectivetopologically, adverbtopologist, 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

Scientific definitions for topology

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 © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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