Geodesic
(HM)-Spaces and Measurable Cardinals
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 53-57

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A locally convex space E is called an (HM)-space if E has invariant nonstandard hulls. In this paper we prove that if E is an (HM)-space, then E is a T(μ)-space, where μ is the first measurable cardinal. This is equivalent to say that in an (HM)-space, with dim(E)≧μ, does not exist a continuous norm. With this result, we prove that there exists an inductive semi-reflexive space E such that the bounded sets in E are finite-dimensional but E is not an (HM)-space. Thus, we answer negatively to an open problem raised up by Bellenot. In this paper, we do not use nonstandard analysis.
DOI : 10.4153/CMB-1984-008-9
Mots-clés : 46A05, 03E55 
Aguirre, José A. Facenda. (HM)-Spaces and Measurable Cardinals. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 53-57. doi: 10.4153/CMB-1984-008-9
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     title = {(HM)-Spaces and {Measurable} {Cardinals}},
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     pages = {53--57},
     year = {1984},
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     number = {1},
     doi = {10.4153/CMB-1984-008-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-008-9/}
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