Nonseparable closed vector subspaces of separable topological vector spaces
The main results proved are the following: (1) For a separable locally convex space \(E\), the product space \(E^c\) has a nonseparable closed vector subspace if and only if \(E\) does not have the weak topology. (2) Every metrizable vector subspace of the product of any number of separable Hausdorff locally convex spaces is separable. (3) The space of all continuous real-valued functions on the classical Michael space \(M\), endowed with the topology of pointwise convergence, is separable, but contains a nonseparable closed vector subspace.
scientific article; zbMATH DE number 6677794
scientific article