query: Using the "open cover" definition of compactness to show that $[0,1]$ is compact
positive_passages.docid: 47903
positive_passages.text: How to prove every closed interval in R is compact?
negative_passages.docid: 142901
negative_passages.text: "The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
negative_passages.docid: 51914
negative_passages.text: Show that $S$ is compact.
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 63529
negative_passages.text: How to show that this set is compact in $\ell^2$
negative_passages.docid: 63701
negative_passages.text: An example of a regular function over an open set
negative_passages.docid: 83311
negative_passages.text: Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
negative_passages.docid: 128730
negative_passages.text: Open subspaces of locally compact Hausdorff spaces are locally compact
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 36315
negative_passages.text: Is $[0,1]$ a countable disjoint union of closed sets?
negative_passages.docid: 103451
negative_passages.text: Show that $Y$ is locally compact.
negative_passages.docid: 121626
negative_passages.text: Every open cover of the real numbers has a countable subcover (Lindelöf's lemma)
negative_passages.docid: 106957
negative_passages.text: Compact sets are closed?
negative_passages.docid: 102048
negative_passages.text: Closure of a compact set in Regular space $ X $
negative_passages.docid: 114813
negative_passages.text: Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
negative_passages.docid: 26215
negative_passages.text: Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.