Is the Definition of a Topological Space Paradoxical?

[NateTG]

I don't think that Differential Geometry requires a strong background in topology, but my experience with Differential Geometry hasn't exactly been the best, so someone else should probably comment on that.

http://math.ucr.edu/home/baez/

might help with your quest for information.

 

[bmegun]

T is not a subset of X. T is a collection of subsets of X. In other words, T is a set of sets. Your first reply said this in a fancy way, by stating that T is a subset of the power set of X. To be a topology, T must contain at least two elements: X itself, and the empty set. If T contains only these two sets, it is called the indiscreet topology
for X. If T contains all subsets of X, i.e., the entire power set, then T is called the
discreet topology. Interesting topologies associated with X are usually between these two extremes.

 

[chroot]

Just learn differential geometry and tensor calculus, and you'll be set for a good into to GR. There are many good books on the topic; I like one called "A Short Course on General Relativity" by Nightingale.

- Warren

 

[mathwonk]

this discussion persuades me that the art of reading books is hopelessly lost. anyone who read even a few pages of a mediocre book on topology would not have any of these questions.

web based learning is obviously a satanic invention of the powers of ignorance, superstition, and darkness!