Fibre tensor product bundles

Authors:
Bernard R. Gelbaum and Athanasios Kyriazis

Journal:
Proc. Amer. Math. Soc. **93** (1985), 675-680

MSC:
Primary 46M05; Secondary 46M20

DOI:
https://doi.org/10.1090/S0002-9939-1985-0776201-1

MathSciNet review:
776201

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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.

**[1]**N. Bourbaki,*Theory of sets*, Addison-Wesley, Reading, Mass., 1968.**[2]**-,*Topologie générale*, Chapitre X, Hermann, Paris, 1961.**[3]**James Dugundji,*Topology*, Allyn and Bacon, Inc., Boston, Mass., 1966. MR**0193606****[4]**B. R. Gelbaum,*Tensor products over Banach algebras*, Trans. Amer. Math. Soc.**118**(1965), 131–149. MR**0178371**, https://doi.org/10.1090/S0002-9947-1965-0178371-7**[5]**Bernard R. Gelbaum,*Banach algebra bundles*, Pacific J. Math.**28**(1969), 337–349. MR**0244763****[6]**Athanasios Kyriazis,*On the spectra of topological 𝐴-tensor product 𝐴-algebras*, Yokohama Math. J.**31**(1983), no. 1-2, 47–65. MR**734158****[7]**-,*Locally convex algebra bundles*(to appear).**[8]**Anastasios Mallios,*On the spectrum of a topological tensor product of locally convex algebras*, Math. Ann.**154**(1964), 171–180. MR**0165382**, https://doi.org/10.1007/BF01360889**[9]**-,*General theory of topological algebras: selected topics*(to appear).**[10]**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**

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0776201-1

Article copyright:
© Copyright 1985
American Mathematical Society