query: The torus is connected
positive_passages.docid: 157002
positive_passages.text: Connected compact covering space of torus is homeomorphic to $S^1\times S^1$
negative_passages.docid: 108394
negative_passages.text: Proof of that every interval is connected
negative_passages.docid: 4642
negative_passages.text: Morphing a "sheet of paper" into a torus
negative_passages.docid: 116866
negative_passages.text: $A\times B$ connected component implies $A,B$ connect components
negative_passages.docid: 87152
negative_passages.text: The difference between the algebraic torus and the geometric torus
negative_passages.docid: 64060
negative_passages.text: Is it possible to obtain a sphere from a quotient of a torus?
negative_passages.docid: 102297
negative_passages.text: Construction of a regular pentagon
negative_passages.docid: 108857
negative_passages.text: Torus with semi-dashed line in TikZ
negative_passages.docid: 154990
negative_passages.text: Fundamental group of two tori with a circle ($S^1✕${$x_0$}) identified
negative_passages.docid: 108864
negative_passages.text: Showing that two topologies give rise to the same topology
negative_passages.docid: 151735
negative_passages.text: $\mathbb{R}^3 \setminus A$ deformation retracts onto $S^1 \vee S^2$
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 111838
negative_passages.text: Prove that a standard torus is diffeomorphic to $ \mathbb S^1\times \mathbb S^1$
negative_passages.docid: 72211
negative_passages.text: Isomorphism involving Eilenberg-Maclane space, Tors.
negative_passages.docid: 63697
negative_passages.text: connected subspaces need to lie in one separated component
negative_passages.docid: 84654
negative_passages.text: The graph of xy = 1 is connected or not
negative_passages.docid: 64021
negative_passages.text: Fundamental group of a torus with points removed