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| ``Re: point''
by alozano on 2006-07-25 14:25:35 |
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| A point is not necessarily embedded in a topological space. One of the most interesting applications of the object "point" come from the so-called finite geometries, which have been studied to great extent. (One considers a geometry with some finite number of points and some set of lines between them; e.g. these can be constructed so they become counterexamples to well-known axioms).
So I think that "point" should be defined in more generality. However, in my opinion, this is a truly difficult definition... Maybe one should follow Euclid: a point is that which has no part, a line is breadthless length, ...
Alvaro |
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