Talk:Closed Topologist's Sine Curve is not Path-Connected

Rename?

Steen and Seebach use "Topologist's Sine Curve" for $G \cup \{(0,0)\}$, the closed topologist's sine curve is the one we need here, and then the "extended topologist's sine curve" is the closed one along with the segment from $(0,1)$ to $(1,1)$. Although I don't like S&S as a source for general topological terminology, I think they're probably definitive on counterexample nomenclature. --Dfeuer (talk) 16:44, 12 January 2013 (UTC)

I just created Definition:Topologist's Sine Curve. It's a bit of a mess, so feel free to try to make it better. --Dfeuer (talk) 16:50, 12 January 2013 (UTC)

Wikipedia agrees with S&S, while PlanetMath and Munkres' Topology (if memory serves me right) use "Topologist's Sine Curve" for $G \cup J$. So we can choose our own definition.

I agree that using "Topologist's Sine Curve" is more descriptive than "Graph of Sine of Reciprocal". I'll have a look at your definition. --Anghel (talk) 16:52, 12 January 2013 (UTC)

Alternative proof

I quick glance at S & S suggests they have what looks to be a much simpler proof using local connectedness. --Dfeuer (talk) 17:02, 12 January 2013 (UTC)

Feel free to add it. --prime mover (talk) 22:06, 12 January 2013 (UTC)

Renaming

The renaming has been done according to the terminology in Steen & Seebach. Seriously, it's a worthy work. --prime mover (talk) 17:52, 18 January 2018 (EST)