query: Prove that if $Y$ is compact then $X$ is compact
positive_passages.docid: 150379
positive_passages.text: Perfect Map $p:\ X\to Y$, $Y$ compact implies $X$ compact
negative_passages.docid: 49994
negative_passages.text: Deduction of $\forall y \exists x (x=y)$
negative_passages.docid: 69650
negative_passages.text: In $\mathbb{R}^n$, locally lipschitz on compact set implies lipschitz
negative_passages.docid: 12467
negative_passages.text: Why does this proof work: Closed unit ball in $C_0$ is not compact
negative_passages.docid: 16948
negative_passages.text: Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
negative_passages.docid: 43376
negative_passages.text: If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
negative_passages.docid: 99645
negative_passages.text: Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
negative_passages.docid: 138607
negative_passages.text: Proof that a limit point compact metric space is compact.
negative_passages.docid: 47668
negative_passages.text: Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
negative_passages.docid: 14219
negative_passages.text: Is the intersection of a closed set and a compact set always compact?
negative_passages.docid: 117781
negative_passages.text: Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition
negative_passages.docid: 144589
negative_passages.text: Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
negative_passages.docid: 135157
negative_passages.text: Totally bounded, complete $\implies$ compact
negative_passages.docid: 64694
negative_passages.text: $C_{c}(X)$ is complete. then implies that $X$ is compact.
negative_passages.docid: 58948
negative_passages.text: If $A$ is compact, is then $f(A)$ compact?
negative_passages.docid: 51853
negative_passages.text: $K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
negative_passages.docid: 22464
negative_passages.text: Which of the following subsets of   $\mathbb{R}^2$ are compact