query: In a normed space $E$, is the convex envelope of any compact set also compact?
positive_passages.docid: 156101
positive_passages.text: Is the convex hull of closed set in $\mathbb R^{n}$ is closed?
negative_passages.docid: 17336
negative_passages.text: Least norm in convex set in Banach space
negative_passages.docid: 118045
negative_passages.text: Is the Baire space $\sigma$-compact?
negative_passages.docid: 38761
negative_passages.text: Is the $ L^{p}$$[0,1]$ norm continuous in p?
negative_passages.docid: 73074
negative_passages.text: $f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
negative_passages.docid: 19566
negative_passages.text: Continuous images of compact sets are compact
negative_passages.docid: 60521
negative_passages.text: Continuity of a convex function
negative_passages.docid: 31559
negative_passages.text: If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
negative_passages.docid: 147213
negative_passages.text: Prove that finite unions of compact sets are compact
negative_passages.docid: 139272
negative_passages.text: On the norm of a quotient of a Banach space.
negative_passages.docid: 146146
negative_passages.text: Proof that a closed subset of a compact space is a compact space
negative_passages.docid: 54764
negative_passages.text: Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 7345
negative_passages.text: Is $C[0,1]$ a Banach space for the $L^1$ norm?
negative_passages.docid: 144656
negative_passages.text: Linear functional and a bounded norm
negative_passages.docid: 142740
negative_passages.text: If $\varphi \in E'$ and $A$ is convex and open then $\varphi (A)$ is an open interval
negative_passages.docid: 30423
negative_passages.text: interior points and convexity