Is $V$ infinite-dimensional?
92510
Proving a vector space is infinite-dimensional
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
44738
Compact operators on an infinite dimensional Banach space cannot be surjective
26329
Is there a shape with infinite area but finite perimeter?
16647
Is the world $C^\infty$?
126136
Fundamental question about dimensional analysis
74024
Higher dimensional equivalent of complex numbers
34206
Quadratic form under $\mathbb{C}$ finite-dimension vector space always have a nonzero vector that yields zero?
95004
Infinite Volume but Finite Surface Area
28238
A question about long exact sequence of finite dim vector spaces
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
155621
Finiteness of the dimension of a normed space and compactness
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
112910
Is the set of real numbers really uncountably infinite?
60692
Is this map to a finite dimensional topological vector space an open map?
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