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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 $p$ 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

   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