$C(X)$ is finite dimensional iff $X$ is finite
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
17378
Characterize finite dimensional algebras without nilpotent elements
70785
A finite Hausdorff space is discrete
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
122814
Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
39351
$f(X)$ is uncountable and hence $X$ is uncountable.
3810
When is a function a dimension?
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
17495
Show that the vector space of all continuous real-valued functions is infinite-dimensional
78256
Finite additivity in outer measure
102042
If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
47810
$C(X)$ is separable when $X$ is compact?
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
157585
Structure theorem of finite rings
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant