So what's the actual point of topology?

>>7948175

to study mathematical physics to study portals

>>7948180
I prefer unmathematical physics actually. Sure it may never give us a means to make portals but at least we can discuss the philosophy of them.

>>7948175
to be pointless

It is real analysis generalized to whatever set

>>7948211
topology is not analysis, analysis just uses basic topology

>>7948175
you need topology for tons of things, from analysis to geometry.

>>7948211
that's measure theory you nitwit

>>7948186
Underrated post

To let us all live like kings lived 300 years ago.

Studies structures and properties preserved under continuous deformation.

/thread

>>7948317
>/threading your own post
>"topology studies topology :^)"

>>7948175
Generalizes several important concepts from geometry and set theory.
Also, it's just damn cool.

>>7948301
Here's your (You)

>>7948211
If you're going to be an analyst about it, at least say something kek worthy like "to motivate an introduction to sigma algebras."

>>7948175
what else am i supposed to masturbate to

>>7948386
Meh, you can't topologically distinguish a BBW from a model, riemannian geometry is better from that pov

Topology is only good for maps. There are no other applications (besides the extra-dimensional travel through rips in the quantum foam).

>>7948229
>topology is not analysis, analysis just uses basic topology
Spoken like a man who has never taken PDE

>>7948175
It gives a really neat way to talk about points being "close together" even when there is no notion of distance in your space.

>>7948853
whats a pdf

>>7948186
This would make sense if the question was:
>what's the actual point of locales?

>>7948175
For me there are two min applications of topology. First if wwe are talking about point-set topology, then the main use of it in fields like analysis ist the extension of notion of continuity of a map. Since continuity of a function f:R->R actually means that, if the points x,y are close, then f(x) and f(y) are close, to define continuity of maps between general spaces X and Y you need to give a definition of points x, x' being close to each other in X ang points y, y' being close to eacch other in Y. And this is exaclty what point set topology does, this is the point of defining the topology on X (so the set of all open sets).

Now the second aplication is the algebraic topology, So to actually explain the point of algebraic topology first lets think about what is the actual point of geometry. So consider R^2, the things that you are concerd with when you are talking about geometry on R^2 are angels between line segments in R^2, and the ratio of the lenghts of the line segments. Now there is a special class of transformations of R^2 that perserve angels and ratios, namly the affine transformations of the plane. So actually you could say that the geometry of R^2 is actually the study of the invariants of affine transformation. Now in algebraic topology you also study the invariants of a class of maps between two topological spaces X and Y, but instead of taking the affine transformations, you take the class of all continouos transformations between X and Y.