Topology

Topology (from Greek τόπος - "place" and λόγος - "study") is a the branch of mathematics that studies the propeties of objects that are preserved through continuous deformations (such as stretching, compression and hogging). "Continuous" means that ruptures (breaking of the object's integrity) and splicing (matching object's points) do not happen. Topology grew out of geometry, but unlike geometry, topology is not concerned with metric properties such as distances between points. Instead, topology involves the study of properties that describe how a space is assembled, such as connectedness and orientability. Topology lies in the search for solution of a problem relating to the geometry of position in the true sense of the term.

History
Topology started to develop in 18th century, when Leonhard Euler solved Seven Bridges of Königsberg in 1736. The term "topology" was firstly used by Johann Benedict Listing. Modern topology depends strongly on the ideas of set theory, developed by Georg Cantor in the later part of the 19th century. Henri Poincaré published Analysis Situs in 1895, introducing the concepts of homotopy and homology, which are now considered part of algebraic topology.

Properties
Two main properties of topology is homeomorphism and homotopy equivalence.