Introduction to topology
The first thing we must do is firmly put down any notion you may have that we’re about to start making maps. The only thing topology and topography have in common is their derivation from the Greek τoπoσ, or space. Topology is a relatively new field of mathematics and is related to geometry. In both of these subjects one studies the shape of things. In geometry, one characterizes, for example, a can of pineapple by its height, radius, surface area, and volume. In topology, one tries to identify the more subtle property that makes it impossible to get the pineapple out of the tin, no matter what shape it is battered into, as long as one does not puncture the can.
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