Geodesic
Fragmentability of the Dual of a Banach Space with Smooth Bump
Serdica Mathematical Journal, Tome 24 (1998) no. 2, pp. 187-198

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We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.
Keywords: Smooth Bump, Fragmentability, Sigma-Fragmentability 
@article{SMJ2_1998_24_2_a5,
     author = {Kortezov, I.},
     title = {Fragmentability of the {Dual} of a {Banach} {Space} with {Smooth} {Bump}},
     journal = {Serdica Mathematical Journal},
     pages = {187--198},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_1998_24_2_a5/}
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Kortezov, I. Fragmentability of the Dual of a Banach Space with Smooth Bump. Serdica Mathematical Journal, Tome 24 (1998) no. 2, pp. 187-198. http://geodesic.mathdoc.fr/item/SMJ2_1998_24_2_a5/