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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 1st 2019

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJun 20th 2022

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJun 20th 2022
• (edited Jun 20th 2022)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 20th 2022

• Ioan Mackenzie James: Fibrewise topology, Cambridge Tracts in Mathematics, Cambridge University Press (1989) $[$ISBN:9780521360906$]$
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJun 20th 2022

Also added pointer to Booth & Brown.

Then I sub-divided the list of references into “Exponential law for parameterized topological spaces” and references on parameterized homotopy theory proper.

Finally I made the first of these lists an !include-file, since it is needed also elsewhere.

As a result there is now a little overlap between the two lists. But that shouldn’t hurt.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJun 20th 2022

I have recorded (in a new section, here) the definition of fiberwise mapping spaces and the fact that their construction preserves Hurewicz fibrations.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJun 20th 2022

added the remark (here) that the fiberwise mapping space construction does not in general preserve weak Hausdorffness

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJun 20th 2022

made explicit (here) that the fiber of the fiberwise mapping space is the mapping space of the fibers

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeJun 21st 2022

$Map \big( p_B^\ast X_0 ,\, p_B^\ast A_0 \big) \;\simeq\; p_B^\ast Map\big(X_0,\, A_0\big)$