TOPOLOGY
CONCEPT OF TOPOLOGY: offshoot of geometry that originated during the 19th century and that studies those properties an object retains under deformation—specifically, bending, stretching and squeezing, but not breaking or tearing. Thus, a triangle is topologically equivalent to a circle but not to a straight line segment. Similarly, a solid cube made of modeling clay could be deformed into a ball by kneading. It could not, however, be molded into a solid torus (ring) unless a hole were bored through it or two surfaces were joined together. A solid cube is therefore not topologically equivalent to a finger ring.
BRANCHES
GENERAL T.
TOPOLOGICAL GROUPS AND DIFFERENTIAL T.
ALGEBRAIC T.
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