How can embed separable Banach to Cb(X)(family of all bounded continuous functions on topological space X) with non metrizable X ? If X is locally compact or Tychonof is very well.
note : We know that there exists an isometrically isomorphic between any Banach H and H^ (H^ is second dual of H or H^=H**) and know by Kuratofski theorem we can make an isometrically isomorphic between H and Cb(H).
But we want a topological space X that is not metrizable because i want Cech-stone extension an Cech-stone compactification is not metrizable in general?