query: $q:X\to Y$ continuous, show that $X$ is compact
positive_passages.docid: 150379
positive_passages.text: Perfect Map $p:\ X\to Y$, $Y$ compact implies $X$ compact
negative_passages.docid: 155923
negative_passages.text: continuity of $f(x,y)$ in $\mathbb R^2$.
negative_passages.docid: 55749
negative_passages.text: Compactly supported continuous function is uniformly continuous
negative_passages.docid: 128069
negative_passages.text: Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
negative_passages.docid: 28637
negative_passages.text: Proving continuous image of compact sets are compact
negative_passages.docid: 5881
negative_passages.text: $\sqrt x$ is uniformly continuous
negative_passages.docid: 121957
negative_passages.text: Is $p\mapsto \|f\|_p$ continuous?
negative_passages.docid: 7081
negative_passages.text: isometry $f:X\to X$ is onto if $X$ is compact
negative_passages.docid: 14578
negative_passages.text: Proving that an additive function $f$ is continuous if it is continuous at a single point
negative_passages.docid: 16735
negative_passages.text: If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
negative_passages.docid: 19111
negative_passages.text: If every real-valued continuous function is bounded on $X$ (metric space), then $X$ is compact.
negative_passages.docid: 18040
negative_passages.text: Show that a compact metric space is bounded
negative_passages.docid: 36227
negative_passages.text: Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
negative_passages.docid: 83494
negative_passages.text: Uniform continuity of $\ln(x)$
negative_passages.docid: 15727
negative_passages.text: show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
negative_passages.docid: 116663
negative_passages.text: If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
negative_passages.docid: 34344
negative_passages.text: Is a function that maps every compact set to a compact set continuous?