added (here) the statement that pullback of fiberwise mapping spaces exhibits a closed functor.

]]>added (here) the example

$Map \big( p_B^\ast X_0 ,\, p_B^\ast A_0 \big) \;\simeq\; p_B^\ast Map\big(X_0,\, A_0\big)$ ]]>made explicit (here) that the fiber of the fiberwise mapping space is the mapping space of the fibers

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

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

]]>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.

]]>added pointer to:

- Ioan Mackenzie James:
*Fibrewise topology*, Cambridge Tracts in Mathematics, Cambridge University Press (1989) $[$ISBN:9780521360906$]$

added pointer to:

- L. Gaunce Lewis, Jr.,
*Open maps, colimits, and a convenient category of fibre spaces*, Topology and its Applications**19**1 (1985) 75-89 $[$doi.org/10.1016/0166-8641(85)90087-2$]$

added pointer to:

- Michael C. Crabb, Ioan Mackenzie James:
*Fiberwise homotopy theory*, Springer Monographs in Mathematics, Springer (1998) $[$doi:10.1007/978-1-4471-1265-5, pdf ,pdf$]$

added pointer to

- Vincent Braunack-Mayer,
*Combinatorial parametrised spectra*(arXiv:1907.08496)