query: Give an example of a topological space $X$ such that $\pi_1(X)=S_3$.
positive_passages.docid: 75157
positive_passages.text: Every Group is a Fundamental Group
negative_passages.docid: 94018
negative_passages.text: Homology groups of $\mathbb{R}^3\setminus \ S^1$ and $\mathbb{R}^3\setminus E^1_+$
negative_passages.docid: 28766
negative_passages.text: Intuition behind topological spaces
negative_passages.docid: 106298
negative_passages.text: Prove that some topology is not metrizable
negative_passages.docid: 70082
negative_passages.text: Show: Quotient space is homeomorphic to unit sphere
negative_passages.docid: 46408
negative_passages.text: Show that the Hausdorff topology is unique in a finite set $X$
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 129943
negative_passages.text: Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
negative_passages.docid: 115190
negative_passages.text: Why is physical space equivalent to $\mathbb{R}^3$?
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 14322
negative_passages.text: Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
negative_passages.docid: 139827
negative_passages.text: On which topological spaces, can we give a group structure to make it a topological group?
negative_passages.docid: 79213
negative_passages.text: Proof about a Topological space being arc connect
negative_passages.docid: 107076
negative_passages.text: Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
negative_passages.docid: 145415
negative_passages.text: Examples of almost compact spaces.
negative_passages.docid: 85870
negative_passages.text: Show this set is a base for some topology on $\mathbb{Z}$
negative_passages.docid: 57653
negative_passages.text: Relation between line bundles over $\mathbb{P}^1$ in geometry and topology