Geodesic
On bornological products
Glasgow mathematical journal, Tome 11 (1970) no. 1, pp. 37-40

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

It is well known that, provided that the indexing set I is not too large, the productof a family of bornological locally convex topological vector spaces Eαis bornological. Products of bornological spaces were first studied by Mackey [3]. He reduced the problem to the study of R1, showing that this space is bornological if and only if I satisfies a certain condition, related to a problem in measure theory posed by Ulam [5]. We shall therefore call it the Mackey-Ulam condition on I. A similar study of the spaces R1 is to be found in the paper [4] by Simons; see also [1, Ch. IV, §6, exercise 3]. 
Robertson, A. P. On bornological products. Glasgow mathematical journal, Tome 11 (1970) no. 1, pp. 37-40. doi: 10.1017/S0017089500000811
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[1] 1.Grothendieck, A., Espaces vectoriels topologiques (Sãao Paulo, 1958). Google Scholar

[2] 2.Iyahen, S. O., Semiconvex spaces II, Glasgow Math. J. 10 (1969), 103–105. Google Scholar | DOI

[3] 3.Mackey, G. W., Equivalence of a problem in measure theory to a problem in the theory of vector lattices, Bull. Amer. Math. Soc. 50 (1944), 719–722. Google Scholar | DOI

[4] 4.Simons, S., The bornological space associated with R1, J. London Math. Soc. 36 (1961), 461–473. Google Scholar | DOI

[5] 5.Ulam, S., Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 140–150. Google Scholar | DOI

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