Topology

>>8636827
Lee, Introduction to Topological Manifolds

munkres

>>8636827
Here are the links if you haven't read them before

http://www.southalabama.edu/mathstat/personal_pages/carter/Dugundji.pdf

https://ia800501.us.archive.org/16/items/GeneralTopology/Kelley-GeneralTopology_text.pdf

http://webmath2.unito.it/paginepersonali/sergio.console/Dispense/topology%20%202Ed%20-%20James%20Munkres.pdf

>>8636831
It looks like it goes in a different direction from the others, not sure if it will help me out

>>8636834
Why?

>>8636844
>Why?

it's the only one i've read

>>8636850
Fair enough, it does look like it goes faster than Dugundji

>>8636834
This. I used it, it's good. Also as far as im aware (could be wrong) this is the standard text for first topology course.

what are the prereqs to study topology? its the only reason im considering a math major. is it even that interesting?

>>8638733

Point-set Topology: Intro to Proofs. Set Theory or Real Analysis would be helpful but not required.

>>8638747
ok thanks

hey guys, what do you think about distributions? Is it cool i mean is it worth to study it ?

>>8638733
technically there are no prerequisites apart from set theory, but really if you learn topology without having done analysis upto things like poitnwise convergeance and uniform convergeance then you're being a dumbass>>8638733

also if you're considering being a maths major just because of a subdiscipline you know nothing about you're a retard

>>8636827
>general topology

If you -really- only have those three, go with Munkres. I'd recommend grabbing Willard, though.

>>8639208
The others weren't readily avalaible online or were in french, so yeah. I'll post the program later and see if I can get more books on them

File: 1481792774650.png (1MB, 2960x2090px) Image search: [Google]

1MB, 2960x2090px

>>8639223
topos theory
Topology via Logic
https://ncatlab.org/nlab/show/locale

>>8639223
>>8639407
Here it is
>Axiom of choice, cardinals, ordinals
>Metric spaces
>Topological spaces
>Topological vector spaces, Banach spaces

I already know a fair bit of vector, Banach and Hilbert spaces, duality, convexity, etc. I also know about the axiom of choice but I've only worked with Zorn's lemma when proving stuff like separation theorems and the like.

Is the program any good? Any other books you think would be useful?

>>8640300
I forgot the book
Frames and Locales:Topology Without points [for classical maths]
http://www.paultaylor.eu/ASD/
https://homotopytypetheory.org/book/

and little intro [begin here]
http://pointlesstopology.com/the-point-of-pointless-topology.pdf
http://www2.math.uu.se/~palmgren/Trieste.pdf
http://www.cse.chalmers.se/~coquand/pos.pdf
http://www.cse.chalmers.se/~coquand/formal.html

then
and those two intros for the correspondence, through spectra, algebra<>topology
https://en.wikipedia.org/wiki/Stone_duality
https://ncatlab.org/nlab/show/Stone+duality

then here
"Topology via Logic" by Vickers
+ Frames and Locales:Topology Without points [for classical maths]
-remember that frames are about doing point free topology in classical maths
-locales are about doing point free topology in constructive predicative maths
-stick to point free topology as much as you can and do point-set topology as much predicatively constructively as you can [meaning avoid choice, avoid universal quantification over non compact spaces, careful with exponentiation]

>>8640341
and this cannot hurt
https://arxiv.org/abs/1303.5631
>It is well known that axiom of choice implies the existence of non-measurable sets for Lebesgue's measure on R as well as the existence of "paradoxical" decompositions of the unit ball of R^3 (Banach-Tarski). This is generally interpreted as the price to be paid for the numerous services provided by this axiom. The theory proposed by Olivier Leroy shows that we can have simultaneously axiom of choice and " everything is measurable " it takes place within the framework of "locales" which are particular cases of Grothendieck's toposes : a "locale" is just a poset which has the formal properties of the poset of open subsets of a topological space. "Locales" have already been the object of numerous studies (cf for example "Sheaves in Geometry and Logic" of S.Mac Lane and I.Moerdijk. Springer 92.). One of the remarkable aspects of this theory is that it applies in a relevant way to the usual topological spaces in which it shows up " non standard sub-spaces " (sub-locales)); with for consequence that the intersection (in the meaning of locale) of ordinary sub-spaces is not anymore necessarily a (ordinary) sub-space. We have for example a sub-locale of R (called generic sub-locale of R) which is the intersection of dense open sets and which is still dense (although pointless). The most striking result is doubtless that the natural continuation of the measure of Lebesgue (on [0,1] for example) on the open sets to the totality of sub-locales of [0,1] is a sigma additive outside regular measure The "paradoxical " partitions which gave non-measurable subsets in the classical context are no more partitions in the context of locales. There are hidden intersections.... Jean-Malgoire et Christine Voisin


for constructive algebra
http://hlombardi.free.fr/liens/constr.html