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Proceedings of the American Mathematical Society

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On the number of separable locally convex spaces


Authors: Lech Drewnowski and Robert H. Lohman
Journal: Proc. Amer. Math. Soc. 58 (1976), 185-188
MSC: Primary 46A05
DOI: https://doi.org/10.1090/S0002-9939-1976-0417728-6
MathSciNet review: 0417728
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Abstract: The number of distinct separable locally convex spaces is shown to be $ {2^{{2^c}}}$. The number of distinct separable and complete, or metrizable, or normed locally convex spaces is shown to be $ {2^c}$. There is no separable locally convex space that is quotient-universal for the class of separable locally convex spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0417728-6
Keywords: Locally convex space, separable space, quotient-universal space
Article copyright: © Copyright 1976 American Mathematical Society

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