Definition talk:Alexandroff Extension

This is also known as the Alexandroff compactification. I suppose such a name is preferred? --barto (talk) 15:26, 26 January 2017 (EST)

Good call -- we prefer definitions and theorems tied to a particular name on $\mathsf{Pr} \infty \mathsf{fWiki}$ purely Because. --prime mover (talk) 18:22, 26 January 2017 (EST)

... but is it the Alexandroff compactification or Alexandroff compactification topology? Please use your judgment, I'm not familiar enough with this. --prime mover (talk) 18:24, 26 January 2017 (EST)

In fact, the topological space itself is called Alexandroff extension. Its topology (set of open sets) may be referred to as Alexandroff extension topology, but I don't think that should be the name of the page and I wonder if anyone uses that combination of words.

Note: Under certain conditions, the Alexandroff extension is a compactification in which case it can be called Alexandroff compactification.

In summary, I propose to name it Alexandroff extension (like Wikipedia does) and add redirects for all of its aliases. --barto (talk) 02:20, 27 January 2017 (EST)

Job done. --prime mover (talk) 03:08, 27 January 2017 (EST)

Not sure about the redirect from Alexandroff compactification if the two are not completely synonymous -- it would be preferable to have a separate page for the latter and further material (either on the page itself or as a separate theorem page, whatever is appropriate) added to explain what the differences are and in what circumstances they are indeed equivalent. --prime mover (talk) 03:11, 27 January 2017 (EST)

Maybe. For the moment, I'd leave it as is. If someone feels like writing more about it in the future, they may feel free about changing it. --barto (talk) 08:11, 28 January 2017 (EST)