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"A primer on mapping class groups" authors defined the topology on $\overline{\mathbb{H}^2}$. I am unable to visualize the open sets there. I would appreciate it if someone helps me to understand the topology on $\overline{\mathbb{H}^2}$. Thank you in advance.

Lokenath Kundu
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    This question is probably better suited to math.stackexchange. In this context the compactification of the upper half plane is homeomorphic to the closed disk. It may be easier for you to visualize compactification in the Poincare model of hyperbolic space by applying the Cayley transform to the upper half plane. – Neal Sep 11 '22 at 16:52
  • How good is your topology? Do you understand the concept of "subspace topology"? – Lee Mosher Sep 13 '22 at 12:08
  • Yes, I do understand subspace topology. Is that come directly from there? Still, I have a problem understanding the topology of $\overline{\mathbb{H}^2}$. – Lokenath Kundu Sep 14 '22 at 16:19

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