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 definitions 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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.
   • CommentAuthorDmitri Pavlov
   • CommentTimeNov 6th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Definition A map $p$ of [[topological spaces]] is a __Serre microfibration__ if for any lifting square for $\{0\}\times K\to [0,1]\times K$ and $p$, we can find $\epsilon>0$ such that the lifting property is satisfied after restricting to $[0,\epsilon]\times K\subset [0,1]\times K$. ## Properties Any [[Serre fibration]] is a Serre microfibration. Any inclusion of [[open subspaces]] is a Serre microfibration. It is a Serre fibration if and only it is a [[homeomorphism]]. ## Related concepts * [[microflexible sheaf]] * [[h-principle]] * [[Serre fibration]] <a href="https://ncatlab.org/nlab/revision/Serre+microfibration/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Serre+microfibration">current</a>

   Created:

   Definition

   A map of topological spaces is a Serre microfibration if for any lifting square for and , we can find such that the lifting property is satisfied after restricting to .

   Properties

   Any Serre fibration is a Serre microfibration.

   Any inclusion of open subspaces is a Serre microfibration. It is a Serre fibration if and only it is a homeomorphism.

   Related concepts

   • microflexible sheaf

   • h-principle

   • Serre fibration

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeApr 27th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: ## References * [[George Raptis]], _On Serre microfibrations and a lemma of M. Weiss_, Glasgow Mathematical Journal 59:3 (2017), 649-657. [doi](http://dx.doi.org/10.1017/s0017089516000458). <a href="https://ncatlab.org/nlab/history/show/Serre+microfibration/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Serre+microfibration">current</a>

   Added:

   References

   • George Raptis, On Serre microfibrations and a lemma of M. Weiss, Glasgow Mathematical Journal 59:3 (2017), 649-657. doi.

   v3, current

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeApr 27th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: The original definition (in the more general context of [[quasitopological spaces]]) is Definition 1.4.2.B in * [[Mikhael Gromov]], _Partial Differential Relations_, Springer, 1986. <a href="https://ncatlab.org/nlab/history/show/Serre+microfibration/4">v4</a>, <a href="https://ncatlab.org/nlab/show/Serre+microfibration">current</a>

   Added:

   The original definition (in the more general context of quasitopological spaces) is Definition 1.4.2.B in

   • Mikhael Gromov, Partial Differential Relations, Springer, 1986.

   v4, current