query: $Y\subset X$ is Lindelof iff Every $X$-open cover of $Y$ has a countable $X$-open subcover.
positive_passages.docid: 18423
positive_passages.text: Subspace of Lindelöf space is not Lindelöf: Example
negative_passages.docid: 128118
negative_passages.text: Is the cofinite topology on a countable set first countable?
negative_passages.docid: 79424
negative_passages.text: Don't understand proof that interior of a set is open
negative_passages.docid: 44673
negative_passages.text: $M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time
negative_passages.docid: 152193
negative_passages.text: The intersection of a closure with an open set
negative_passages.docid: 102457
negative_passages.text: for any $A\subseteq X$, $f(\overline{A})\subseteq\overline{f(A)}$ , if and only if $f: X \to Y$ is continuous.
negative_passages.docid: 99236
negative_passages.text: Interior of closure of an open set
negative_passages.docid: 21892
negative_passages.text: Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
negative_passages.docid: 65196
negative_passages.text: Gluing Lemma for Closed Sets: Infinite Cover Counter-Example
negative_passages.docid: 119649
negative_passages.text: Every metrizable space with a countable dense subset has a countable basis
negative_passages.docid: 7678
negative_passages.text: Show "countable complement topology" is a topology
negative_passages.docid: 80096
negative_passages.text: Prove that the union of countably many countable sets is countable.
negative_passages.docid: 44974
negative_passages.text: Infinite set and countable subsets
negative_passages.docid: 149317
negative_passages.text: An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 103769
negative_passages.text: The Cartesian product of a finite number of countable sets is countable
negative_passages.docid: 24699
negative_passages.text: A regular, Lindelöf space is normal