/sci/ - Science & Math

>>9345070
That /sci/ is rapidly declining in quality

>>9292721
>>9292722
I mean that nobody understands the NEET struggles...

Going to go cry. Please be patient I have autism

>>8962029
Nope. I was just throwing ideas around, and those were concentrated the totally disconnected and compact Hausdorff spaces of the form [math]Y^X[/math]. I need to check how your duality works, and then be dissappointed.

>>8850287
Nice, happy birthday! Are you talking about some sort of categorical geometry or something? That would hurt some butts, to defile the holiest part of math with the blasphemous theory of categories!

On those locales, there is, atleast, an equivalence between the category of sober spaces and that of spatial locales. This is both good and bad. I'm interested in seeing homotopy on locales, and the easiest way would be to take the (topological) homotopy applied on their spectra, but this would give no advantage: most of the interesting spaces are sober, and thus homeomorphic to their own spectra. No simplification, nothing! Why this interests me most is that some things can be done in locales with a lot less machinery than they would require in topological spaces, for example, the Tychonoff theorem and the axiom of choice. If this can be done, what else can be? Could this affect homotopy, too? An idea of what could be (if there was a homotopy theory for locales) would be that topological homotopy would imply localic homotopy, which would be comparable to how one proves stuff like that an (n-1)-sphere is not a retract of a closed n-ball, etc., to use a weaker notion to disprove claims about the stronger. Weaker because non-sober spaces can have isomorphic frames even if they are not homeomorphic.

On my own stuff, it's almost done. I'm going to include a corollary that there is a ring for each essentially small abelian category is equivalent to a subcategory of R-mod, etc. Nothing too deep, but stuff I've derived myself.

>>8849712
Pls be patient

I'm starting a microbiology program in the fall. I got a lot of my gen eds done already so my first two years will be pretty light.


I'm thinking of learning some programming on ths side, since it will be beneficial in fhe future. (Bioinformatics and what not)

What languages/things to learn?