topology


to·pol·o·gy

noun \tə-ˈpä-lə-jē, tä-\
plural to·pol·o·gies

Definition of TOPOLOGY

1
:  topographic study of a particular place; specifically :  the history of a region as indicated by its topography
2
a (1) :  a branch of mathematics concerned with those properties of geometric configurations (as point sets) which are unaltered by elastic deformations (as a stretching or a twisting) that are homeomorphisms (2) :  the set of all open subsets of a topological space
b :  configuration <topology of a molecule> <topology of a magnetic field>
to·pol·o·gist \-jist\ noun

Origin of TOPOLOGY

International Scientific Vocabulary
First Known Use: 1850

to·pol·o·gy

noun \tə-ˈpäl-ə-jē, tä-\   (Medical Dictionary)
plural to·pol·o·gies

Medical Definition of TOPOLOGY

2
: configuration 1 <the topology of a molecule>
topo·log·i·cal \ˌtäp-ə-ˈläj-i-kəl\ also topo·log·ic \-ik\ adjective

topology

noun    (Concise Encyclopedia)

In mathematics, the study of the properties of a geometric object that remains unchanged by deformations such as bending, stretching, or squeezing but not breaking. A sphere is topologically equivalent to a cube because, without breaking them, each can be deformed into the other as if they were made of modeling clay. A sphere is not equivalent to a doughnut, because the former would have to be broken to put a hole in it. Topological concepts and methods underlie much of modern mathematics, and the topological approach has clarified very basic structural concepts in many of its branches. See also algebraic topology.

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