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# What is topology?

In general, topology is a branch of mathematics that examines patterns of geometric figures based on position and relative position without regard to size. It has also been called “rubber-sheet” geometry because objects examined in topology are under continuous transformation (also called topological transformation or homeomorphism). The shapes can be stretched, bent, and twisted in various ways, as long as they are not torn or cut as they are changed. For example, a circle is considered to be topologically equivalent to an ellipse (it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. This includes changing an object based on a one-to-one correspondence. (For more about changing such shapes and one-to-one correspondence, see elsewhere in this chapter.)

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