query: Classic applications of Baire category theorem
positive_passages.docid: 81
positive_passages.text: $\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$
negative_passages.docid: 141114
negative_passages.text: Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
negative_passages.docid: 129194
negative_passages.text: Correspondences between Borel algebras and topological spaces
negative_passages.docid: 80787
negative_passages.text: 2-morphisms for 2-category: don't understand how to draw
negative_passages.docid: 102899
negative_passages.text: Category theory with objects as logical expressions over $\{\vee,\wedge,\neg\}$ and morphisms as?
negative_passages.docid: 16534
negative_passages.text: Can $(\Bbb N,\leq)$ have an $\aleph_0$-categorical theory (in a larger language)?
negative_passages.docid: 68786
negative_passages.text: "This property is local on" : properties of morphisms of $S$-schemes
negative_passages.docid: 133413
negative_passages.text: Proof of paracompactness of CW-complexes (J. Lee, Introduction to Topological Manifolds)
negative_passages.docid: 134909
negative_passages.text: Associativty of smash product on compact spaces
negative_passages.docid: 81895
negative_passages.text: A generalisation of the fundamental theorem of algebra
negative_passages.docid: 119256
negative_passages.text: Function $f\in M[G]$, $f:\kappa\to M$ is in the ground model implies $\kappa^+$-Baire
negative_passages.docid: 127886
negative_passages.text: Artin's lemma and some morphisms.
negative_passages.docid: 118045
negative_passages.text: Is the Baire space $\sigma$-compact?
negative_passages.docid: 41180
negative_passages.text: Arbitrary products of quasi-coherent sheaves?
negative_passages.docid: 95187
negative_passages.text: The set of homotopy classes
negative_passages.docid: 139828
negative_passages.text: Finitely Presented Modules and Exact Sequences
negative_passages.docid: 25260
negative_passages.text: Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$