Spaces of partial maps, fibred mapping spaces and the compact-open topology

Arens, 1951, Topologies for function spaces, Pacific J. Math., 1, 5, 10.2140/pjm.1951.1.5 Booth, 1970, The exponential law of maps I, Proc. London Math. Soc., 20, 179, 10.1112/plms/s3-20.1.179 Booth, 1971, The section problem and the lifting problem, Math. Z., 121, 273, 10.1007/BF01109973 Booth, 1971, The exponential law of maps II, Math. Z., 121, 311, 10.1007/BF01109977 Booth, 1973, A unified treatment of some basic problems in homotopy theory, Bull. Am. Math. Soc., 79, 331, 10.1090/S0002-9904-1973-13157-X Booth, 1974 Booth, 1974, Fibrations and cofibred pairs, Math. Scand., 35, 145, 10.7146/math.scand.a-11541 P.I. Booth and R. Brown, On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps. General Topology and Appl. 8 (2) 165–179. Brown, 1961, Some problems in algebraic topology: function spaces, function complexes and FD-complexes, Thesis Brown, 1968 A. Clark, Quasi-topology and compactly generated spaces, Mimeographed Notes, Brown University. Day, 1972, A reflection theorem for closed categories, J. Pure Appl. Algebra, 2, 1, 10.1016/0022-4049(72)90021-7 Dugundji, 1966 Dyer, 1972, An adjunction theorem for locally equi-connected spaces, Pacific J. Math., 41, 669, 10.2140/pjm.1972.41.669 Gabriel, 1967 Hu, 1964 Lundell, 1969 Vogt, 1971, Convenient categories of topological spaces for homotopy theory, Arch. Math., XXII, 546 Wyler, 1973, Convenient categories for topology, General Topology and Appl., 3, 225, 10.1016/0016-660X(72)90014-1