What does "topology" mean?
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).
Topology
/təˈpɒləd͡ʒi/ noun
noun ·Uncommon ·Advanced level
Meaning at a glance
- Primary sense: 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).
- Grammar: topology is listed as noun.
- Nearest alternatives: analysis, analysis situs, arithmetic, dna topology.
- Useful contrasts: geometry, linearization, random layout.
- Usage evidence: A manifold is like a three-layer cake: on the bottom, a set; in the middle, a topology; on top, an atlas.
How to use "topology"
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- Use the example sentence as a context check. If your sentence uses the word differently, confirm that the grammar still fits.
Meaning check
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- Is there enough surrounding context to prevent ambiguity?
Source and review context
This entry combines structured lexical data with WordToolSet review checks. Definitions, examples, synonyms, and usage notes may come from different source tables, so the page is designed to show evidence from more than one angle before you rely on "topology" in a final draft.
If a word has several senses, prefer the sense that matches your sentence's grammar and surrounding context. A correct definition can still be the wrong choice when the sentence needs a different register, emphasis, or level of specificity.
Before you rely on this definition
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Compare nearby meanings
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Definition decision workflow
1. Identify the role
Check whether "topology" is acting as noun in your sentence. A definition is only useful when the grammar matches the way the word is being used.
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Final meaning check
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Definitions
Noun
- 1 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). uncountable
"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."
- 2 the configuration of a communication network wordnet
- 3 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. countable, uncountable
"A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau)."
- 4 the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions wordnet
- 5 The anatomical structure of part of the body. countable, uncountable
Show 6 more definitions
- 6 the study of anatomy based on regions or divisions of the body and emphasizing the relations between various structures (muscles and nerves and arteries etc.) in that region wordnet
- 7 The arrangement of nodes in a communications network. countable, uncountable
- 8 topographic study of a given place (especially the history of the place as indicated by its topography) wordnet
- 9 The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application. countable, uncountable
- 10 The topographical study of geographic locations or given places in relation to their history. countable, uncountable
- 11 The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place. countable, dated, uncountable
Synonyms
All synonymsAntonyms
Example
"A manifold is like a three-layer cake: on the bottom, a set; in the middle, a topology; on top, an atlas."
Common questions
What is a synonym for "topology"?
Common synonyms include: analysis, analysis situs, arithmetic, dna topology, geometric topology, graph topology.
How do you use "topology" in a sentence?
A manifold is like a three-layer cake: on the bottom, a set; in the middle, a topology; on top, an atlas.
How do you pronounce "topology"?
Pronounced /təˈpɒləd͡ʒi/.
Etymology
From Late Latin topologia, from By surface analysis, topo- (“place”) + -logy (“study of, a branch of knowledge”).