Geodesic
A direct sum is holomorphically bornological with the topology induced by a cartesian product
Portugaliae mathematica, Tome 40 (1981) no. 2, pp. 252-256.

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Keywords: holomorphically bornological, holomorphically infrabarreled, holomorphically barreled, inductive limit topology 
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     title = {A direct sum is holomorphically bornological with the topology induced by a cartesian product},
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Barroso, Jorge Alberto; Nachbin, Leopoldo. A direct sum is holomorphically bornological with the topology induced by a cartesian product. Portugaliae mathematica, Tome 40 (1981) no. 2, pp. 252-256. http://geodesic.mathdoc.fr/item/PORMA_1981__40_2_115448/