In a normed space $X$ with field $\mathbb{R}$, is $\{ x \in X \mid \|x\| =1\}$ compact in general?
59697
Is the boundary of the unit sphere in every normed vector space compact?
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
26215
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
67625
$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$
63608
Cauchy sequence in a normed space
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
45249
Pseudocompactness does not imply compactness
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
95993
Isn't every subset of a compact space compact?
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
98756
Unit ball in $C[0,1]$ not sequentially compact
84492
Can $X$ have compact connected components?
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
10531
Is the convex hull of a compact set compact?
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded