Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 26th 2021
   • (edited Jan 26th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexWe had (still have) a proof of the contractibility of some version of $S^\infty$ in the Definition-section at _[[n-sphere]]_. Since that doesn't seem to be the right place for that material, and in order to make it easier to link to $S^\infty$ and its contractibility, I am giving it its own page here. In creating this page, I have: * copied over the material of the section _[n-sphere -- Definition -- Infinite-dimensional sphere](https://ncatlab.org/nlab/show/sphere#InfiniteDimensionalSphere)_; * expanded out the first paragraph into a new Idea-section here; * added a section with the definition as a colimit over relative cell complex inclusions and the quick proof of weak contractibility from that. So the previous discussion in terms of infinite-dimensional unit spheres in LCTVSs and/or in shift spaces is currently both here as well as inside _[[n-sphere]]_. But I suggest we remove it at the latter place, and just leave the link to this new page here. <a href="https://ncatlab.org/nlab/revision/infinite-dimensional+sphere/1">v1</a>, <a href="https://ncatlab.org/nlab/show/infinite-dimensional+sphere">current</a>

   We had (still have) a proof of the contractibility of some version of $S^\infty$ in the Definition-section at n-sphere.

   Since that doesn’t seem to be the right place for that material, and in order to make it easier to link to $S^\infty$ and its contractibility, I am giving it its own page here.

   In creating this page, I have:

   • copied over the material of the section n-sphere – Definition – Infinite-dimensional sphere;

   • expanded out the first paragraph into a new Idea-section here;

   • added a section with the definition as a colimit over relative cell complex inclusions and the quick proof of weak contractibility from that.

   So the previous discussion in terms of infinite-dimensional unit spheres in LCTVSs and/or in shift spaces is currently both here as well as inside n-sphere. But I suggest we remove it at the latter place, and just leave the link to this new page here.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJan 26th 2021
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexSomething I wondered about reading this page is whether the topology coming from the $l^2$ norm coincides with the coherent/colimit topology. I am told this follows from something called the Banach-Dieudonne theorem. Does anyone have more information on this?

   Something I wondered about reading this page is whether the topology coming from the $l^2$ norm coincides with the coherent/colimit topology. I am told this follows from something called the Banach-Dieudonne theorem. Does anyone have more information on this?