# topology

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## to·pol·o·gy

(tō-pol'ŏ-jē),
1. Synonym(s): regional anatomy
2. The study of the dimensions of personality.
[topo- + G. logos, study]

## topology

(tə-pŏl′ə-jē)
n. pl. topolo·gies
1. Topographic study of a given place, especially the history of a region as indicated by its topography.
2. Medicine The anatomical structure of a specific area or part of the body.
3. Mathematics
a. The study of certain properties that do not change as geometric figures or spaces undergo continuous deformation. These properties include openness, nearness, connectedness, and continuity.
b. The underlying structure that gives rise to such properties for a given figure or space: The topology of a doughnut and a picture frame are equivalent.
4. Computers The arrangement in which the nodes of a network are connected to each other.

to·pol′o·gist n.

## topology

(tō-pŏl′ō-jē)
1. In obstetrics, the relationship of the presenting fetal part to the pelvic outlet.
2. In mathematics, the study of the relationships between objects that share a surface or a common border.
References in periodicals archive ?
This simple world, topologists say, is "singly connected."
The coordinates [u.sub.i] in [Mathematical Expression Omitted] are well suited for most of the needs of algebraic topologists - unfortunately, as our formulas will make clear, it would be rather complicated to explicitly determine the action of [S.sub.n] on u and the [u.sub.i]'s directly from the definition.
This viewpoint may sometimes seem fanciful: For example, to a topologist, a doughnut and a coffee cup represent the same shape since each has one hole.
Topologists classify the helicoid as a "complete embedded minimal surface of finite topology with infinite total curvature." The word embedded indicates that the surface doesn't fold back on itself.
One early procedure was discovered in 1967 by Bernard Morin, a blind topologist at the Louis-Pasteur University in Strasbourg, France.
Similarly, topologists, using appropriate invariants, can also examine in greater detail what manifolds look like and how one may be transformed into another.
By studying the steps required to transform one shape into another, topologists establish relationships between different shapes and learn the key differences distinguishing one shape from another.
Topologists emphasize the properties of shapes that remain unchanged, no matter how much the shapes are stretched, twisted or molded so long as they aren't torn or cut.
If the universe as a whole is a quantummechanical system like an atom and is in its ground state, then, according to Hawking, it no longer needs a singularity at the beginning, and the centers of black holes are no longer singularities but little separate universes connected to ours by passages that topologists call wormholes.

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