Mathematics-Topology

Feb 3rd, 2012
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Northwestern University
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As mathematics continues to expand so will topology. Topology will most likely give way to even more complex and abstract areas of mathematics. It is hard to imagine what may be the next branch of topology, considering that much of this field can only be explained mathematically. It is exciting to think that eventually these principles might have real life applications in a time when we are comfortable dealing with more than three dimensional space.

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Subject- MathematicsTopic-TopologyUniversity Name- Northwestern UniversityTopologyMathematics is a field so vast and diverse that it is impossible to be an expert in all areas. It is also a field that is constantly evolving and branching outward. The field of topology is one of the newest intensively studied branches of mathematics. "A simple way to describe topology is as rubber sheet geometry" [2]. "Topology is an 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" [1]. Under these conditions, one could say that a square is topologicallyequivalentto a circle because a square can be bent and stretched into a circle [3]. However, a square is not topologically equivalent to a torus because a torus cannot be formed unless a hole is bored through the medium, or two pieces are joined together. Topologists obviously have expanded upon these simple concepts over time to create theorems further removed from our ordinary experiences. Some of these shapes and objects exist in fourdimensionalspace or higher dimensions and cannot exist inour world. Theoretically these shapes would be as commonplace as a tree or rock in a higher dimensional universe. However, in our universe topologists turn to mathematics to understand these shapes [6].The first mathematical problem, which led to the origins

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