query: Compactness, why is $(0,1)$ not compact? I need the "thought process"
positive_passages.docid: 114813
positive_passages.text: Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
negative_passages.docid: 147331
negative_passages.text: Compactness and Hausdorffness
negative_passages.docid: 25752
negative_passages.text: What should be the intuition when working with compactness?
negative_passages.docid: 50611
negative_passages.text: Question about Stone-Čech compactification
negative_passages.docid: 22854
negative_passages.text: Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
negative_passages.docid: 64694
negative_passages.text: $C_{c}(X)$ is complete. then implies that $X$ is compact.
negative_passages.docid: 1756
negative_passages.text: 1-point compactification and embedding
negative_passages.docid: 71011
negative_passages.text: Criteria of compactness of an operator
negative_passages.docid: 5392
negative_passages.text: Compact support vs. vanishing at infinity?
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 106534
negative_passages.text: "Closed subsets of compact space are compact" with an alternative definition of covering
negative_passages.docid: 74147
negative_passages.text: Compactness of  Multiplication Operator on $L^2$
negative_passages.docid: 29303
negative_passages.text: Cartesian product of compact sets is compact
negative_passages.docid: 81927
negative_passages.text: Example of closed and bounded in $\mathbb Q$ set that is not compact
negative_passages.docid: 29474
negative_passages.text: Compactness of $\operatorname{Spec}(A)$
negative_passages.docid: 100476
negative_passages.text: Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
negative_passages.docid: 153107
negative_passages.text: Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?