Every separable Banach space embeds in $C[0,1]$.
136439
Where can I read the full proof of the Banach-Mazur theorem?
137067
For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.
28731
Banach space in functional analysis
73154
Compact subset in colimit of spaces
81929
d-metrizable spaces are sequential
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
6955
A Banach space is reflexive if and only if its dual is reflexive
156161
Banach-Tarski theorem without axiom of choice
127522
Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable
109632
Show reflexive normed vector space is a Banach space
104881
Showing that two Banach spaces are homeomorphic when their dimensions are equal.
98756
Unit ball in $C[0,1]$ not sequentially compact
87897
Bounded operators on separable Hilbert spaces
51177
When are two norms equivalent on a Banach space?
44738
Compact operators on an infinite dimensional Banach space cannot be surjective
41620
The dual space of $c$ is $\ell^1$
8334
A reflexive Banach space is separable iff its dual is separable