topology

American  

[tuh-pol-uh-jee] / təˈpɒl ə dʒi /

Rarely analysis situs

noun

Mathematics.

topologies plural

1. the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching.

2. Also called point set topology.  the study of limits in sets considered as collections of points.

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

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topology British  

/ ˌtɒpəˈlɒdʒɪk, təˈpɒlədʒɪ /

noun

1. the branch of mathematics concerned with generalization of the concepts of continuity, limit, etc

2. Former name: analysis situs.  a branch of geometry describing the properties of a figure that are unaffected by continuous distortion, such as stretching or knotting

3. maths a family of subsets of a given set S, such that S is a topological space

4. the arrangement and interlinking of computers in a computer network

5. the study of the topography of a given place, esp as far as it reflects its history

6. the anatomy of any specific bodily area, structure, or part

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topology Scientific  

/ tə-pŏl′ə-jē /

1. 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.

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Other Word Forms

• topologic
  adjective
• topological
  adjective
• topologically
  adverb
• topologist
  noun

Etymology

Origin of topology

First recorded in 1650–60; topo- + -logy

Explanation

Topology is a kind of math — it's the study of shapes that can be stretched and moved while points on the shape continue to stay close to each other In the branch of geometry known as topology, two objects are equivalent if you can make them resemble each other by stretching, bending, or twisting them. This makes sense if you imagine two rubber bands: you can manipulate them into squares or ovals, and they are still the same. In computer science, topology refers to the way elements of a network are arranged. And in the 1650s, topology was the study of "the location where plants are found."

Example Sentences

The researchers also found that once the topology goes beyond two dimensions, it can no longer be described by a single number.

From Science Daily • Mar. 21, 2026

The findings, published in Nature Communications, show that measuring the OAM of two entangled photons reveals an intrinsic topology, a fundamental feature of the entanglement itself.

From Science Daily • Mar. 21, 2026

His rejection of England’s imperial mythology is Romantic in its passion for philology and topology.

From The Wall Street Journal • Jan. 23, 2026

While optimization can indirectly address some security vulnerabilities, the assets unique to quantum computing, such as circuit topology, encoded data or hardware coded intellectual property systems generally lack end-to-end protection.

From Science Daily • Jan. 20, 2026

Claytor’s dissertation topic, regarding point-set topology, delighted the Penn faculty and was acclaimed by the mathematical world as a significant advance in the field.

From "Hidden Figures" by Margot Lee Shetterly

Related Words

• earth science
• geology
• geopolitics
• topography