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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 1st 2016

at Serre fibration I have spelled out the proof that that with $F_x \hookrightarrow X \overset{fib}{\to} Y$ then $\pi_\bullet(F) \to \pi_\bullet(X)\to \pi_{\bullet(Y)}$ is exact in the middle. here.

(This is intentionally the low-technology proof using nothing but the definition. )

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 18th 2017

Added to Serre fibration a section Properties – Relation to Hurewicz fibrations with pointer to

a) counter-example of a Serre fibration that is not a Hurewicz fibration

b) statement that all Serre fibrations between CW-complexes are Hurewicz fibrations.

Also added to the Examples-section pointer to the homotopy lifting property for covering spaces.

• CommentRowNumber3.
• CommentAuthorDavidRoberts
• CommentTimeJul 19th 2017

(The projection map of) a fibre bundle over any paracompact space, or more generally, a bundle that admits a trivialisation over a numerable cover, is a Hurewicz fibration, I believe.. In general, all fibre bundles are Serre fibrations.

(I was torn between adding this comment here or at the covering space thread)

• CommentRowNumber4.
• CommentAuthorDexter Chua
• CommentTimeJul 29th 2017

Fixed some syntax errors

• CommentRowNumber5.
• CommentAuthorTim_Porter
• CommentTimeDec 29th 2018

The ’in particulars’ were ’breeding thick and fast’ in certain parts of this page! I removed one of them to keep the population down.