In the mathematical field of topology, a homeomorphism or topological isomorphism (from the Greek words homoios = similar and μορφή (morphē) = shape = form (Latin deformation of morphe)) is a special isomorphism between topological spaces which respects topological properties. Two spaces with a homeomorphism between them are called homeomorphic. From a topological viewpoint they are the same.
Roughly speaking, a topological space is a geometric object, and the homeomorphism is a continuous stretching and bending of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not. An often-repeated joke is that topologists can't tell the coffee cup from which they are drinking from the donut they are eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.
Intuitively, a homeomorphism maps points in the first object that are "close together" to points in the second object that are close together, and points in the first object that are not close together to points in the second object that are not close together. Topology is the study of those properties of objects that do not change when homeomorphisms are applied.
Reference:
http://en.wikipedia.org/wiki/Homeomorphic
