nLab exponential law for parameterized topological spaces -- references

Exponential law for parameterized topological spaces

On exponential objects (internal homs) in slice categories of (compactly generated) topological spaces – see at parameterized homotopy theory):

• Peter I. Booth, The Exponential Law of Maps I, Proceedings of the London Mathematical Society s3-20 1 (1970) 179-192 $[$doi:10.1112/plms/s3-20.1.179$]$

• Peter I. Booth, The exponential law of maps. II, Mathematische Zeitschrift 121 (1971) 311–319 $[$doi:10.1007/BF01109977$]$

• Peter I. Booth, Ronnie Brown, Spaces of partial maps, fibred mapping spaces and the compact-open topology, General Topology and its Applications 8 2 (1978) 181-195 $[$doi:10.1016/0016-660X(78)90049-1$]$

• Peter I. Booth, Ronnie Brown, On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps, General Topology and its Applications 8 2 (1978) 165-179 $[$doi:10.1016/0016-660X(78)90048-X$]$

• L. Gaunce Lewis, Jr., §1 of: 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$]$

And with an eye towards parameterized homotopy theory:

• Ioan Mackenzie James: §II.9 in: Fibrewise topology, Cambridge Tracts in Mathematics, Cambridge University Press (1989) $[$ISBN:9780521360906$]$

• Peter May, Johann Sigurdsson, §1.3.7-§1.3.9 in: Parametrized Homotopy Theory, Mathematical Surveys and Monographs, vol. 132, AMS 2006 (ISBN:978-0-8218-3922-5, arXiv:math/0411656, pdf)