On the number of separable locally convex spaces

Lech Drewnowski, Robert H. Lohman
1976 Proceedings of the American Mathematical Society  
The number of distinct separable locally convex spaces is shown to be 22°. The number of distinct separable and complete, or metrizable, or normed locally convex spaces is shown to be 2C. There is no separable locally convex space that is quotient-universal for the class of separable locally convex spaces.
doi:10.1090/s0002-9939-1976-0417728-6 fatcat:jhteveucu5fkrb6vrds3qjpgoy