We prove several stability properties for the class of compact Hausdorff spaces $T$ such that $C(T)$ with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.
@article{119081, author = {Ivaylo S. Kortezov}, title = {Function spaces in the Stegall class}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {40}, year = {1999}, pages = {259-270}, zbl = {0979.54020}, mrnumber = {1732646}, language = {en}, url = {http://dml.mathdoc.fr/item/119081} }
Kortezov, Ivaylo S. Function spaces in the Stegall class. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 259-270. http://gdmltest.u-ga.fr/item/119081/
Osnovy Obshchei Topologii v Zadachah i Uprazhneniah (in Russian), Moskva, 1974. | MR 0445439
Une classe d'espaces co-Namioka, C.R. de l'Acad. des Sci., Paris, t.310, série I, 1990, pp.779-782. | MR 1054296
The class of co-Namioka compact spaces is stable under product, Proc. Amer. Math. Soc. 194 3 (1996), 983-986. (1996) | MR 1326999 | Zbl 0844.54016
Gâteaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces, John Wiley & Sons, Inc., 1997. | MR 1461271 | Zbl 0883.46011
Borel selectors for upper semi-continuous set-valued maps, Acta Math. 56 (1985), 41-7. (1985) | MR 0793237 | Zbl 0588.54020
A generic factorization theorem, Mathematika 42 (1995), 56-66. (1995) | MR 1346672 | Zbl 0827.54012
Fragmentability of function spaces, preprint.
The Banach-Mazur game and Baire category theorem, in: Contributions to the Theory of Games, vol.III, Annals of Math. Studies 39, Princeton, N.J., 1957, pp.159-163. | MR 0093741
A class of topological spaces and differentiability, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen 10 (1983), 63-77. (1983) | MR 0730947