Introduction to topology

Abstract

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.

“when George drew out a tin of pineapple from the bottom of the hamper...we felt that life was worth living after all...there was no tin-opener to be found...I took the tin off myself and hammered at it till I was worn out and sick at heart, whereupon Harris took it in hand. We beat it out flat; we beat it back square; we battered it into every form known to geometry — but we could not make a hole in it. Then George went at it, and knocked it into a shape, so strange, so weird, so unearthly in its wild hideousness, that he got frightened.”

Jerome K. Jerome