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Topology studies properties of spaces that are invariant under any continuous deformation.

It is sometimes called "rubber-sheet geometry" because the objects can be stretched
and contracted like rubber, but cannot be broken.

For example, a square can be deformed into a circle without breaking it,
but a figure 8 cannot. Hence a square is topologically equivalent to a circle,
but different from a figure 8.

https://uwaterloo.ca/pure-mathematic...at-is-topology