query: Interior of a convex set
positive_passages.docid: 30423
positive_passages.text: interior points and convexity
negative_passages.docid: 94231
negative_passages.text: Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
negative_passages.docid: 129081
negative_passages.text: Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
negative_passages.docid: 113594
negative_passages.text: Convex combination of quasiconvex functions.
negative_passages.docid: 15645
negative_passages.text: Is convex open set in $\mathbb{R}^n$ is regular?
negative_passages.docid: 10531
negative_passages.text: Is the convex hull of a compact set compact?
negative_passages.docid: 72659
negative_passages.text: How can we define convexity in one dimension?
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: 73338
negative_passages.text: Prove that the closure of complement, is the complement of the interior
negative_passages.docid: 66151
negative_passages.text: Solving inequality for convex functions.
negative_passages.docid: 77217
negative_passages.text: Proof that a coordinate-wise convex function is convex?
negative_passages.docid: 157572
negative_passages.text: The distance between two sets inside euclidean space
negative_passages.docid: 101190
negative_passages.text: Extreme Points of a Convex Hull
negative_passages.docid: 33527
negative_passages.text: Star convex set is simply connected.
negative_passages.docid: 35857
negative_passages.text: Characterization of log-convexity
negative_passages.docid: 158399
negative_passages.text: Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
negative_passages.docid: 79424
negative_passages.text: Don't understand proof that interior of a set is open