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1. • CommentRowNumber1.
   • CommentAuthorTom
   • CommentTimeDec 8th 2013
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   Author: Tom
   Format: MarkdownItexI am reading the article on [Hurewicz connection](http://ncatlab.org/nlab/show/Hurewicz+connection) Theorem. A map $\pi:E \to B$ is a Hurewicz fibration iff there exists at least one Hurewicz connection for $\pi_!$. I have two questions: (1) How to formally construct the Hurewicz connection for $\pi_!$ ? (2). It has scratched an idea of proof. May I know if anyone can reference a completed formal proof to me. (a paper or an article will be great !).

   I am reading the article on Hurewicz connection

   Theorem. A map $\pi:E \to B$ is a Hurewicz fibration iff there exists at least one Hurewicz connection for $\pi_!$.

   I have two questions:

   (1) How to formally construct the Hurewicz connection for $\pi_!$ ?

   (2). It has scratched an idea of proof. May I know if anyone can reference a completed formal proof to me. (a paper or an article will be great !).

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 8th 2013
   • (edited Dec 8th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexHey Tom, maybe hold it for a second. It seems you just posted this question five times to the nForum and at least two more times ([here](http://math.stackexchange.com/questions/597417/on-dold-fibration) and [here](http://math.stackexchange.com/questions/597368/on-nlab-hurewicz-connection)) to Math.Stack exchange. I'll reply in this one thread here and (assuming you are not a bot) would ask you to stick to this one thread here. Now what exactly is it you are after? The nLab page _[Hurewicz connection](http://ncatlab.org/nlab/show/Hurewicz+connection)_ spells out a proof of the statement that the existence of such characterizes Hurewicz fibrations. Let us know if you find this proof needs more explanation or the like. You may or may not profit from reading it, but you should know that there is the original article available here: * [[Witold Hurewicz]], _On the concept of fiber space_, Proc. Nat. Acad. Sci. USA __41__ (1955) 956--961; MR0073987 (17,519e) [PNAS,pdf](http://www.pnas.org/content/41/11/956.full.pdf). I find that a decent review of these matters is in this article here, which you can find online on GoogleBooks: * [[James Eells]], Jr., _Fibring spaces of maps_, in Richard Anderson (ed.) _Symposium on infinite-dimensional topology_, 1972

   Hey Tom,

   maybe hold it for a second. It seems you just posted this question five times to the nForum and at least two more times (here and here) to Math.Stack exchange.

   I’ll reply in this one thread here and (assuming you are not a bot) would ask you to stick to this one thread here.

   Now what exactly is it you are after? The nLab page Hurewicz connection spells out a proof of the statement that the existence of such characterizes Hurewicz fibrations. Let us know if you find this proof needs more explanation or the like.

   You may or may not profit from reading it, but you should know that there is the original article available here:

   • Witold Hurewicz, On the concept of fiber space, Proc. Nat. Acad. Sci. USA 41 (1955) 956–961; MR0073987 (17,519e) PNAS,pdf.

   I find that a decent review of these matters is in this article here, which you can find online on GoogleBooks:

   • James Eells, Jr., Fibring spaces of maps, in Richard Anderson (ed.) Symposium on infinite-dimensional topology, 1972
3. • CommentRowNumber3.
   • CommentAuthorTom
   • CommentTimeDec 8th 2013
   • PermaLink
   Author: Tom
   Format: MarkdownItexUrs: Thanks. I am running through the above references. In addition, I have another question: How to construct the Hurewicz connection? The first part of the scratched proof did construct the connection based upon the assumption that fibration exists from the diagram. So I am thinking how to establish the condition: how to create the connection first.

   Urs:

   Thanks. I am running through the above references. In addition, I have another question: How to construct the Hurewicz connection? The first part of the scratched proof did construct the connection based upon the assumption that fibration exists from the diagram. So I am thinking how to establish the condition: how to create the connection first.