Topology
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Topology is the area of mathematical study dealing with the properties of objects that are preserved through deformation, twisting, and stretching without tearing or glueing. The objects studied are called Topological Spaces.

For example, if you're not allowed to tear or glue, but just allowed to deform, then a coffee cup (which has a single hole) can be distorted and moulded into a ring doughnut, but can never be distorted and moulded into a ball, or a sugar bowl (which has two handles). There's no way to get rid of the hole, and there's no way to get a second hole.

Topology comes in two flavours: "Point Set Topology" and "Algebraic Topology"

Related topics are Braid Theory and Knot Theory.

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