Show that if X is a normed linear space, then any finite-dimensional subspace M of X must be closed.
91173
Finite-dimensional subspace normed vector space is closed
125623
Subspaces of separable normed spaces
33642
Finite dimensional subspace of $C([0,1])$
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
140813
How do i prove that continuous linear transformation between normed spaces is bounded?
158523
Topology: Proof that a finitely generated cone is closed
98391
example of a nonempty subset is closed under scalar multiplication but not a subspace
73254
spectral radius in normed space is subadditive.
73353
Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?
145222
The dual of subspace of a normed space is a quotient of dual: $X' / U^\perp \cong U'$
155621
Finiteness of the dimension of a normed space and compactness
98759
Proof of "Dual normed vector space is complete"
109632
Show reflexive normed vector space is a Banach space
88185
Proof that a subspace $A$ of a complete metric space $X$ is complete iff $A$ is closed
45252
"Every linear mapping on a finite dimensional space is continuous"
19415
Proof that every finite dimensional normed vector space is complete
53850
Proof that every normed vector space is a topological vector space