Isometric embeddings of separable Banach spaces into (^∞ c)∪\0\

The classical Banach--Mazur theorem asserts that every separable Banach space admits an isometric embedding into $C[0,1]$. It is also well known that every separable Banach space embeds isometrically into ^∞. We show that such an embedding can be chosen so that its image intersects c only at the origin. Moreover, we prove that any finite- or countable-dimensional, or more generally separable, subspace of (^∞ c)∪\0\ can be extended to a subspace containing an isometric copy of an arbitrary separable Banach space, while still avoiding c. We further establish that this extension property also holds for every subspace D⊂ ^∞ with D∩ c=\0\ and separable image in the quotient ^∞/c.