Geodesic
Iteration of Ultraproducts of Locally Convex Spaces
Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 55 .

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Let $\{E_{ij}:(i,j)\in I\times J\}$ be a family of locally convex Hausdorff spaces. We study the relation between the spaces $P_{(i,j)\in I\times J}(E_{ij})$ and $P_{j\in J}(P_{i\in I}(E_{ij}))$. In particular, we prove that the ultraproduct of an ultraproduct is again an ultraproduct.
Classification : 46A05 46Q05 
@article{PIM_1993_N_S_54_68_a8,
     author = {Jos\'e Antonio Facenda Aguirre},
     title = {Iteration of {Ultraproducts} of {Locally} {Convex} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {55 },
     publisher = {mathdoc},
     volume = {_N_S_54},
     number = {68},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a8/}
}
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José Antonio Facenda Aguirre. Iteration of Ultraproducts of Locally Convex Spaces. Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 55 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a8/