topology

American  

[tuh-pol-uh-jee] / təˈpɒl ə dʒi /

Rarely analysis situs

noun

Mathematics.

plural

topologies

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

"What's exciting about our work is that we combine the three big topics in modern condensed matter physics in a single experiment: strong interactions between the electrons, topology and dynamical control," Imamoğlu says.

From Science Daily • Mar. 3, 2026

A recent major study assessed efficiency of brain networks, essentially how the brain is wired, through white matter topology.

From Science Daily • Feb. 19, 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

Over time, curiosity won out, and Diana Kirschbaum began looking for experimental signs of topology.

From Science Daily • Jan. 15, 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