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Let $ R$ be a Noetherian normal domain, and let $ R^+$ denote the absolute integral closure of $ R$ , i.e. the directed union of all module-finite extension domains. I’m trying to understand what “separable” should mean for elements of $ R^+$ . It’s hard to say what “should mean” means, exactly, but let’sRead more

It is straightforward to check that for any separable Hilbert space $ H$ , the cardinal number of $ B(H)$ is of continuum. I am asking the same question concerning separable Banach spaces. I feel even there exists a separable Banach space whose cardinal number is $ 2^c$ where $ c$ is the cardinal ofRead more

I’m reading up on the theory behind support vector machines and would like a good reference with some general results about linear separability. Specifically, questions like below: Given two finite $ A$ , $ B \subset \mathbb{R}^n$ , of cardinality $ k$ , must there always exist a linear separation, even when $ k >Read more