Quotes About Topology

Topology is destiny,' he said, and put the drawers on. One leg at a time.

Fraa Jad took the garment from me and discovered how the fly worked. "Topology is destiny," he said, and put the drawers on.

Topology is destiny

An organizing frame provides a topology for the space it organizes; that is, it provides a set of organizing relations among the elements in space. When two spaces share the same organizing frame, they share the corresponding topology and so can easily be put into correspondence. Establishing a cross-space mapping between inputs becomes straightforward.

Topologically, men and women are identical. Some things are just larger and more developed in one than the other and positioned differently.

Topology allows the possibility of making qualitative predictions when quantitative ones are impossible.

starting from any topological space, we construct an algebraic object, in this case a group. If two spaces are homeomorphic, then their fundamental groups (and higher homotopy groups) must be isomorphic. This is richer than the original idea of just measuring the number of holes, since a group contains more information than just a number.

One can also use compactifications to view the continuous as the limit of the discrete: for instance, it is possible to compactify the sequence / 2,/ 3,/ 4, . . . of cyclic groups in such a way that their limit is the circle group = /.

OSPF's backbone area is Area 0, and every other area we create must contain a router that has a physical or logical interface in Area 0.

Topologists are not concerned with angles and lengths, which are clearly altered by stretching the rubber sheet, but they do care about more fundamental properties.

In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything.

Most problems I work on are related to geometric structures on surfaces and their deformations.

The usefulness of mathematics allows us to build spaceships and investigate the geometry of our universe. Numbers may be our first means of communication with intelligent alien races. Some physicists have even speculated that an understanding of higher dimensions and of topology-the study of shapes and their interrelationships-may someday allow us to escape our universe, when it ends in either great heat or cold, and then we could call all of space-time our home.

It is as if one hemisphere of your brain is perceiving the world as reflected in a mirror. Through a mirror. See? So left becomes right, and all that that implies. And we don't know yet what that does imply, to see the world reversed like that. Topologically speaking, a left-hand glove is a right-hand glove pulled through infinity.

DEFINITION 1-2. The set S has a topology (or is topologized) provided that, for every point p in S and every subset X of S, the question "Is p a limit point of X?" can be answered.

Calabi-Yau manifold