Talk:Spherically complete field
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open balls?
[edit]The topological field of real numbers is locally compact, but the decreasing sequence of balls given by the open intervals (0, 1/n) has empty intersection.
Therefore, while in the non-archimedean case, open and closed balls can be interchangeably used, is this still true in the archimedean case, or might it be necessary to stipulate open balls? — Preceding unsigned comment added by 179.235.134.104 (talk) 23:57, 19 March 2019 (UTC)
- Unless I'm wrong, on the contrary, this example shows that one should stipulate closed balls! (As you say, R is spherically complete since locally compact.) — MFH:Talk 16:39, 20 June 2019 (UTC)
why only fields?
[edit]Why has Wikipedia "spherically complete" only for fields? This notion makes sense in any metric space, doesn't it? — MFH:Talk 16:42, 20 June 2019 (UTC)
Can you create a spherical completion of any normed field?
[edit]The article does not mention circumstances when one may create a spherical completion of a field that is not already spherically complete.
That would be a very useful addition to this article.