query: Is a topological space $X$ the colimit of an open cover $\cup U_i$ in this way?
positive_passages.docid: 22298
positive_passages.text: Categorical Pasting Lemma
negative_passages.docid: 152193
negative_passages.text: The intersection of a closure with an open set
negative_passages.docid: 102924
negative_passages.text: Normal space- equivalent condition: $\forall U, V$ - open $: U \cup V = X \ \ \ \exists F \subset U \ , G \subset V$ - closed $: F \cup G = X$
negative_passages.docid: 79424
negative_passages.text: Don't understand proof that interior of a set is open
negative_passages.docid: 60053
negative_passages.text: Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
negative_passages.docid: 47680
negative_passages.text: Prove that the union of the interior of a set and the boundary of the set is the closure of the set
negative_passages.docid: 27998
negative_passages.text: Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
negative_passages.docid: 111008
negative_passages.text: Show that $X $ is a infinite set ,it is connected in the finite complement topology?
negative_passages.docid: 157987
negative_passages.text: Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?
negative_passages.docid: 99236
negative_passages.text: Interior of closure of an open set
negative_passages.docid: 147350
negative_passages.text: Homeomorphism between $\prod X_i$ and the Cantor set
negative_passages.docid: 90782
negative_passages.text: Examples of topologies in which all open sets are regular?
negative_passages.docid: 144383
negative_passages.text: The closure of a connected set in a topological space is connected
negative_passages.docid: 60692
negative_passages.text: Is this map to a finite dimensional topological vector space an open map?
negative_passages.docid: 72190
negative_passages.text: Topological proof on discrete topology where $X$ is infinite
negative_passages.docid: 55374
negative_passages.text: Cover of (0,1) with no finite subcover & Open sets of compact function spaces
negative_passages.docid: 128481
negative_passages.text: Can two different topological spaces cover each other?