Dimensionality of a Hilbert Space: Countable or Uncountable?
116143
Ambiguity in number of basis vectors
55230
Dimension of set of commutable matrices
17495
Show that the vector space of all continuous real-valued functions is infinite-dimensional
136909
Functional Analysis: The rank of an operator detemines if it's a compact operator.
58347
$L^p$ spaces and counting measure
30017
Orthogonality and linear independence
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
9295
Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.
1799
How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
50946
Separable Hilbert space have a countable orthonormal basis
155621
Finiteness of the dimension of a normed space and compactness
36184
Countability of disjoint intervals
68006
Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
55691
Are states of a quantum system represented by vectors in a Hilbert space?
72602
Why is important for a manifold to have countable basis?
14550
Every Hilbert space has an orthonomal basis - using Zorn's Lemma
41347
The dimension of the intersection of two vector subspaces