finite dimention subspaces of infinite dimention hilbert space are closed?
52865
Topological Vector Space: $\dim Z\text{ finite}\implies Z\text{ closed}$
22295
Subspace of a separable space is separable
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
87580
Canonical examples of inner product spaces that are not Hilbert spaces?
92510
Proving a vector space is infinite-dimensional
86481
Let $H$ be an infinite-dimensional separable Hilbert space, show that a Hilbert-Schmidt operator is compact
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
125073
Finite-dimensional subspaces of normed vector spaces are direct summands
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
128934
Every infinite Hausdorff space has an infinite discrete subspace
103397
Homeomorphisms between infinite-dimensional Banach spaces and their spheres
153747
Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
91173
Finite-dimensional subspace normed vector space is closed
16692
a representation condition of Hilbert space
1799
How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
69893
An inner product space and its proper closed subspace with trivial orthogonal complement