query: A question about the proof of general lifting theorem in Munkres topology p.479
positive_passages.docid: 152927
positive_passages.text: seemingly nontrivial question about covering maps and evenly covered open sets
negative_passages.docid: 92033
negative_passages.text: Prove that $g$ is a submanifold: $g (t,u,v) = (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)$
negative_passages.docid: 150987
negative_passages.text: Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 148187
negative_passages.text: Question regarding one-point compactification and homeomorphisms
negative_passages.docid: 86308
negative_passages.text: Yoneda-Lemma as generalization of Cayley`s theorem?
negative_passages.docid: 90092
negative_passages.text: Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)
negative_passages.docid: 38226
negative_passages.text: Question about the Riemann-Lebesgue Lemma proof
negative_passages.docid: 108864
negative_passages.text: Showing that two topologies give rise to the same topology
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 46917
negative_passages.text: How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
negative_passages.docid: 133820
negative_passages.text: The product topology on $\mathbb R_d\times \mathbb R$ vs. the dictionary order topology on $\mathbb R\times \mathbb R$
negative_passages.docid: 81550
negative_passages.text: Linking two theorems: on algebraic closure and on minimal splitting field
negative_passages.docid: 101619
negative_passages.text: Question involving the Cauchy-Goursat Theorem
negative_passages.docid: 106434
negative_passages.text: Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
negative_passages.docid: 45179
negative_passages.text: When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
negative_passages.docid: 115502
negative_passages.text: Analogue of the Cantor-Bernstein-Schroeder theorem for general algebraic structures