/sci/ - Science & Math

>>7272055
A bundle of fibres. Fibres are good at "sticking" to each other

A abstraction of a direct product <span class="math">B\times F[/spoiler] in topology, where B and F are good sets.

>>7272055
the fiber bundle is an arrow p:Y->X in the category TOP or LOC


the fiber Y_x over a point x of X is the pullback of the arrow p, along the arrow representing the point x, that is to say, over the arrow x:1->X

the fiber Y_x is then the topological space/locale that hover over x


now, you take a section s of some open U of X

it means that you look at all the fibers Y_x for x in U open in X,

so you take the pullback of Y->X along the subset inclusion U >->X and you get Y_U which is the fiber over U

then a section s is an arrow from U to Y such that p \circ s = the inclusion , that is to say, such that the diagram commutes in TOP or LOC

http://rin.io/swashbuckling-topoi/

>>7272105
Thanks, you're my hero

nlab is a godsend
http://ncatlab.org/nlab/show/fiber+bundle

Since the invention of the hairbrush, I wonder how many orgasms the handles have produced? In Victorian days, when a woman wanting to masturbate to orgasm was considered a form of mental illness. I bet women wore out about three brushes a year, behind the privacy of a locked bathroom door. When things got insane for a woman, and you would go insane, if you never got off, they say a woman went to a doctor and he induced an orgasm (or two, or tree, or four, probably) as a cure for what ailed her. Jesus Christ, the idiotic **** women have endured through the centuries, boggles the ****in mind. It's a damn wonder they even give us any pussy at all.

>>7273328
I just hate people in general

>>7273330
Since the invention of the hairbrush, I wonder how many orgasms the handles have produced? In Victorian days, when a woman wanting to masturbate to orgasm was considered a form of mental illness. I bet women wore out about three brushes a year, behind the privacy of a locked bathroom door. When things got insane for a woman, and you would go insane, if you never got off, they say a woman went to a doctor and he induced an orgasm (or two, or tree, or four, probably) as a cure for what ailed her. Jesus Christ, the idiotic shit women have endured through the centuries, boggles the fuckin mind. It's a damn wonder they even give us any pussy at all.

>>7273299
right so a fiber bundle is a bundle like here >>7272105
but where all fibers are isomorphic in some sense

>>7273331
>being cucked by fiber bundles