Is every basis of an infinite-dimensional vector space with countable basis countable?
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
99599
Uncountable and countable
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
74877
Every metric space with a countable base is separable
154724
Every vector space has a basis
125411
Infinite set always has a countably infinite subset
128437
How to prove that a finite set is countable
119671
Is there an infinite dimensional $V$ such that every linear operator on $V$ is a direct sum of a nilpotent and  an invertible operator?
84830
Vector space of infinite sequences in $\Bbb R$
87692
Basis and dimension of vector space
99656
Prove that the set of all algebraic numbers is countable
92510
Proving a vector space is infinite-dimensional
105358
In a second countable space any base has a countable subset that is still a base
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
67050
Every separable metric space has a countable base
42362
Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals