Fibre tensor product bundles

Gelbaum, Bernard R.; Kyriazis, Athanasios

doi:10.1090/S0002-9939-1985-0776201-1

Fibre tensor product bundles
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by Bernard R. Gelbaum and Athanasios Kyriazis PDF

Proc. Amer. Math. Soc. 93 (1985), 675-680 Request permission

Abstract:

In analogy with fibre bundles, which are locally Cartesian products, fibre tensor product bundles are objects that are locally tensor products. These can be patched together via transition maps, etc., into an object very similar to the set of sections of a locally convex algebra bundle.

References

Theory of sets

Topologie générale

James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
B. R. Gelbaum, Tensor products over Banach algebras, Trans. Amer. Math. Soc. 118 (1965), 131–149. MR 178371, DOI 10.1090/S0002-9947-1965-0178371-7
Bernard R. Gelbaum, Banach algebra bundles, Pacific J. Math. 28 (1969), 337–349. MR 244763
Athanasios Kyriazis, On the spectra of topological $A$-tensor product $A$-algebras, Yokohama Math. J. 31 (1983), no. 1-2, 47–65. MR 734158

Locally convex algebra bundles

Anastasios Mallios, On the spectrum of a topological tensor product of locally convex algebras, Math. Ann. 154 (1964), 171–180. MR 165382, DOI 10.1007/BF01360889

General theory of topological algebras: selected topics

Norman Steenrod, The topology of fibre bundles, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1999. Reprint of the 1957 edition; Princeton Paperbacks. MR 1688579