4 Jan
2010
4 Jan
'10
9:13 a.m.
Hello, I wrote:
Some years ago, a functional analyst needed half an our to prove that homeomorphic Banach spaces have homemorphic duals, a simple consequence of the fact that all functors preserve isomorphisms.
Sorry, I always meant linear homeomorphisms; I missed to say it explicitly. Without linearity, without linearity the statement is false; e.g. the map l_1 -> l_3, (x_n)_n|_> ((x_n)^3)_n is a homeomorphism, but the dual of l_3 is separable, while the dual of l_1 is not. Greetings Reinhard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]