>>> Yeah, topology feels like graduate level math.
>>
>> Trolling++: This is advanced calculus and differential geometry.
>> Topology is much more beautiful, you get it after abstracting
>> those things away which could be related to actual numbers ;)
> 
> do you mean things like genus or number of dimensions?

More like functions operating on R^n so you have actual numerical
coordinates to work with when you start applying the stuff to the
problem of point distances. Topology would more or less say that
all subspaces of R^n with the same finite number m of points are
identical(*), without worrying about coordinates or distances ;)

(*) homeomorphic, the topological notion of "identical": there
     exists a bijective mapping, continuous in both directions.

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