query: Closed Subsets of Compact Spaces Using Subsequences Definition of Compactness
positive_passages.docid: 11114
positive_passages.text: Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
negative_passages.docid: 148994
negative_passages.text: $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
negative_passages.docid: 95993
negative_passages.text: Isn't every subset of a compact space compact?
negative_passages.docid: 148403
negative_passages.text: Compact space and Hausdorff space
negative_passages.docid: 31559
negative_passages.text: If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
negative_passages.docid: 40682
negative_passages.text: What's going on with "compact implies sequentially compact"?
negative_passages.docid: 114608
negative_passages.text: Proof concerning regular space: there exist a closed set contained in any open set containing $x$
negative_passages.docid: 136108
negative_passages.text: Arbitrary intersection of closed, connected subsets of a compact space connected?
negative_passages.docid: 59194
negative_passages.text: Spaces in which "$A \cap K$ is closed for all compact $K$" implies "$A$ is closed."
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 45249
negative_passages.text: Pseudocompactness does not imply compactness
negative_passages.docid: 94485
negative_passages.text: Limit point compactness implies compactness.
negative_passages.docid: 18596
negative_passages.text: A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
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: 158498
negative_passages.text: $A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
negative_passages.docid: 149220
negative_passages.text: If every compact set is closed, then is the space Hausdorff?