>murican's don't see topology or Banach spaces until

canadian here

saw topology in 2nd year and banach spaces in 3rd

i doubt any american school that isn't second-rate teaches it in final year

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624KB, 947x638px

>his university doesn't begin with intro to big number theory

>>8465475
>doing Banach spaces after topology

Huh?
The natural progression is norms > metric spaces > topological spaces, what happened?

>>8465481
>number theory without learning about rings first
Sounds like a stupid university, sorry about that

>>8465492
how do you define a metric space without topological spaces?

i learned about topological spaces in my 2nd year real analysis class (pointset topology, sequences, series, stuff like Heine-Borel)

learned about banach spaces in my 3rd year real analysis class (metric spaces, linear functionals, Hahn-Banach, Jordan-Von Neumann...)

>>8465512
>how do you define a metric space without topological spaces?
nevermind, looked it up, guess it doesn't quite matter which order you do them in

>>8465465
useful for what

>>8465512
>how do you define a metric space without topological spaces?
>"Gee, we just constructed the reals, maybe we should define a function that maps into them, and, like, give it special properties, and call it distance?"
Who the fuck introduces analysis as "a special case of topology"?

>>8465465
I did topology my freshman year in my Analysis on Mflds class.

>>8465512
>pointset topology
Exactly. The definition of a topology is motivated by metric spaces.

>>8465506
Elementary number theory is a good introduction to the motivation for algebraic nt

>>8466267
Elementary number theory uses rings. Anything more elementary than that can be covered in a week in a first term foundations course.

>>8465465
Yeah, thanks Obama.

>>8466843
seriously i texted my vote for hillary on my obama phone and she still didnt win

>>8465465

many don't see topology at all

infact few at my school did