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show/hide this revision's text 2 Fixed latex

I can only point to the place where this was originally done (or rather, the latest edition thereof):

Topology and Groupoids by Ronnie Brown

It's a fantastic textbook and easy to read (and cheap, if you buy the electronic copy - the best £5 I've spent). Ideally what you'd do is calculate the equivalent subgroupoid $\Pi_1(S^1,{a,b,c})$ \Pi_1(S^1,\{a,b,c\})$ where $a,b,c$ are three points in $S^1$, one in each intersection of opens.
show/hide this revision's text 1

I can only point to the place where this was originally done (or rather, the latest edition thereof):

Topology and Groupoids by Ronnie Brown

It's a fantastic textbook and easy to read (and cheap, if you buy the electronic copy - the best £5 I've spent). Ideally what you'd do is calculate the equivalent subgroupoid $\Pi_1(S^1,{a,b,c})$ where $a,b,c$ are three points in $S^1$, one in each intersection of opens.