query: continuous and convex imply the weakly upper semicontinuous
positive_passages.docid: 15924
positive_passages.text: Convexity and strong lower semicontinuity imply weak lower semicontinuity
negative_passages.docid: 149095
negative_passages.text: $f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
negative_passages.docid: 157603
negative_passages.text: Continuity $\iff$ Preimage is closed whenever set is closed
negative_passages.docid: 65346
negative_passages.text: Characterisation of uniformly continuous function
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: 57642
negative_passages.text: Uniform Continuity implies Continuity
negative_passages.docid: 122086
negative_passages.text: continuous function: preimage of closure of a set is closure of preimage
negative_passages.docid: 33129
negative_passages.text: A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for som $T\in B(X,Y)$
negative_passages.docid: 41690
negative_passages.text: Products of Continuous functions: Topology
negative_passages.docid: 126878
negative_passages.text: Monotonic function satisfying darboux property $\Rightarrow$ continuous
negative_passages.docid: 71001
negative_passages.text: Do continuous linear functions between Banach spaces extend?
negative_passages.docid: 32359
negative_passages.text: Inner product of two continuous maps is continuous
negative_passages.docid: 62334
negative_passages.text: Continuity and Joint Continuity
negative_passages.docid: 126759
negative_passages.text: Unbounded continuous function on non-compact metric space
negative_passages.docid: 129757
negative_passages.text: Uniformly convergent implies equicontinuous
negative_passages.docid: 28637
negative_passages.text: Proving continuous image of compact sets are compact