TOPOLOGY

Topology ( Branch of mathematics )
Topology, branch of mathematics
, sometime reffered to as "rubber sheet geometry" in which two ibjects are considered equivalent if they can be continuously deformed into one another through such motions in space as bending, twisting, stretching and shrinking while disallowing tearing apart or gluing together parts. The main topics of interest in topology are the properties that remain unchanged by such continuous deformations.


Topology while similar to geometry differs from geometry in that geometrically equivalent objects often share numerically measured quantities, such as lengths, angles, while topologically equivalent objects resemble each other in a more qualitative sense.

The area of topology dealing with abstract objects is referred to as general, or point set topology. General topology overlaps with another important area of topology called algebraic topology. These areas of specialization form the two major subdisciplines of topology that developed during its relatively modern history.

Topology sub-categories

• General topology: Also called point-set topology, establishes the foundational aspects of topology and investigates properties of topological spaces and concepts inherit to topological spaces.
• Algebraic topology: Tries to measure degree of connectivity using algebraic construct such as homology and homotopy group.
• Differential topology: Dealing with differential functions on differential manifolds.
• Geometric topology: Studies manifolds and their embeddings in other manifolds.