what is topology?

Answer 1

Intuitively, topology is the study of those properties of figures that are preserved under stretching, folding, etc. It is popularly called 'rubber sheet geometry'. The standard joke is that topologists can't tell the difference between a donut and a coffee cup. You see, both of them have one hole and you can imagine extending one side of the donut and pushing in to make a shape like the coffee cup.

Such properties as connectedness (being in one piece), having various types of holes (like the donut) and the number of such holes are topological properties. Another one which is not at all obvious: Imagine your surface divided into regions like countries. If you let F (faces) be the number of countries, E (edges) the number of boundary lines, and V (vertices) the number of places where three or more countries come together, then F-E+V is a topological invariant. For shapes like the basketball or football, this always comes out to be 2. For the donut and the coffee cup, it always comes out to be 0.

If you want a non-intuitive definition of topology, just ask. It will involve set theory though.

Answer 2

Topology is a branch of geometry that deals with those properties of a figure that remain unchanged even when the figure is transformed (bent, stretched) – for example, when a square painted on a rubber sheet is deformed by distorting the sheet.

Topology has scientific applications, as in the study of turbulence in flowing fluids.

The topological theory, proposed in 1880, that only four colours are required in order to produce a map in which no two adjoining countries have the same colour, inspired extensive research, and was proved in 1972 by Kenneth Appel and Wolfgang Haken.


http://www.math.wayne.edu/~rrb/topology.html

Answer 3

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed.

The word topology is derived from a Greek word (topologia) meaning the study of 'place'. The Greek word 'topos' means location or place.

Answer 4

Topology is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation

Answer 5

The study of geometrical properties and spatial relations which remain unaffected by certain changes in shape or size of figures.

Answer 6

it is a method of computer networking, different types are:
star topology
bus topology
etc