topology

[ tuh-pol-uh-jee ]

noun

, Mathematics.

, plural to·pol·o·gies

1. the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching.
2. Also called point set to·pol·o·gy. the study of limits in sets considered as collections of points.
3. a collection of open sets making a given set a topological space.

topology

/ ˌtɒpəˈlɒdʒɪk; təˈpɒlədʒɪ /

noun

1. the branch of mathematics concerned with generalization of the concepts of continuity, limit, etc
2. a branch of geometry describing the properties of a figure that are unaffected by continuous distortion, such as stretching or knotting Former nameanalysis situs
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

topology

/ 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.

Derived Forms

• topologic, adjective
• ˌtopoˈlogically, adverb
• toˈpologist, noun

Other Words From

• top·o·log·ic [top-, uh, -, loj, -ik], top·o·log·i·cal adjective
• top·o·log·i·cal·ly adverb
• to·pol·o·gist noun

Word History and Origins

Origin of topology¹

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

Example Sentences

These principles are governed by the nuanced interplay of stitch patterns, geometry, and yarn topology -- the undercrossings or overcrossings in a knot or stitch.

From Science Daily

"Qin and I showed that using topology," Palmerduca said, "we can modify Wigner's classification for massless particles, giving a description of photons that works in all directions at the same time."

From Science Daily

COFs are a new class of porous, crystalline, purely organic materials with defined topology.

From Science Daily

After publishing breakthrough studies in pattern recognition, string theory and a framework that combined geometry and topology with quantum field theory, Mr. Simons decided to apply his genius to a more prosaic subject — making as much money as he could in as short a time as possible.

From New York Times

That kept the values random -- but random within limits given by constraints of the network topology.

From Science Daily

Related Words

• earth science
• geology
• geopolitics
• topography