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Added a section that introduces those who have not met topology before to it in a non-rigorous way, free of jargon
If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a torus without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.
If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a torus without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.
==Introduction==
Topology is a branch of mathematics. Like geometry, it studies shapes, but it focuses on certain properties of them. For example, length is not a topological property, so to a topologist, a line of length 20 metres and one of length 2 metres are the same. Nor are angles, or curvature, so a topologist would say that triangles and circles are also undistinguishable.
A way of thinking about topology (albeit a non-rigorous one) is that two shapes are topologically the same, if they can be transformed into one another if one can be turned into the other by stretching it (or parts of it), but there must be no cutting of the shape. If you imagine the objects are made of clay then you can stretch or compress the clay or pull it around, but you cannot tear it at any point.
[[category:mathematics]][[Category:Topology]]
[[category:mathematics]][[Category:Topology]]