Geodesic
Connectivity of Function Spaces
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 759-763

Voir la notice de l'article provenant de la source Cambridge University Press

Given two spaces X and Y with Y either an AE (metrizable) or ANE (metrizable), little is known with regard to when the function space (Yx, τ), for some topology τ, is an AE (metrizable) or ANE (metrizable) except when very strong separation properties are imposed on X and Y (see [5, pp. 186-189]). One of our tasks will be to eliminate most of these separation property requirements, therefore complementing or extending some of the results of [5]. We also attach an appendix, which contains some needful information, as well as the complete local analogue of [2, Theorem 5.1].Throughout, we use either the terminology and notation of [2] or of the appendix. We also let co stand for the compact-open topology and pc stand for the pointwise convergence topology of any function space 
Borges, Carlos R. Connectivity of Function Spaces. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 759-763. doi: 10.4153/CJM-1971-084-5
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