query: Show that if $X$ is homotopically equivalent to $Y$, then $\widetilde{X}$ is homotopically equivalent to $\widetilde{Y}$
positive_passages.docid: 156606
positive_passages.text: Universal covering spaces of homotopy equivalent spaces are homotopy equivalent
negative_passages.docid: 108045
negative_passages.text: Show that are logically equivalent
negative_passages.docid: 126881
negative_passages.text: (weak) homotopy equivalence
negative_passages.docid: 42913
negative_passages.text: Equivalence of the definition of the Subbasis of a Topology
negative_passages.docid: 59424
negative_passages.text: Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
negative_passages.docid: 155828
negative_passages.text: How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?
negative_passages.docid: 124829
negative_passages.text: Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell
negative_passages.docid: 105455
negative_passages.text: Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
negative_passages.docid: 156904
negative_passages.text: Homotopy Extension Property: necessary and sufficient condition
negative_passages.docid: 4462
negative_passages.text: Homotopy invariance for cohomology
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: 110729
negative_passages.text: Maps to Sn homotopic
negative_passages.docid: 15312
negative_passages.text: Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
negative_passages.docid: 66895
negative_passages.text: A condition for the image of a metrizable space to be metrizable
negative_passages.docid: 70193
negative_passages.text: Show that the relation defined on an integral domain by "$x\sim y$" ("$x$ is associated with $y$") is a relation of equivalence.
negative_passages.docid: 55488
negative_passages.text: Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
negative_passages.docid: 52548
negative_passages.text: Topological group: Multiplying two loops is homotopic to linking these paths?