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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2013
   • (edited Nov 20th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexthe entry [[profinite space]] and entries related to it were/are a bit in need of some care. The entry used to start out saying "Profinite space is another word for Stone space", which was misleading, because there is a not-entirely-trivial equivalence involved. So I changed it to > A _profinite set_ is a [[pro-object]] in [[FinSet]]. By [[Stone duality]] these are [[equivalence|equivalent]] to [[Stone spaces]] and thus are often called _profinite spaces_. So these are [[compact space|compact]] [[Hausdorff space|Hausdorff]] [[connected space|totally disconnected]] [[topological spaces]]. Also cross-links with [[profinite reflection]] were missing, and so I added them. Also cross-linked with _[[finite set]]_, with _[[localic reflection]]_ and maybe with more. The entry [[profinite space]] is still stubby/unsatisfactory.

   the entry profinite space and entries related to it were/are a bit in need of some care.

   The entry used to start out saying “Profinite space is another word for Stone space”, which was misleading, because there is a not-entirely-trivial equivalence involved. So I changed it to

   A profinite set is a pro-object in FinSet. By Stone duality these are equivalent to Stone spaces and thus are often called profinite spaces. So these are compact Hausdorff totally disconnected topological spaces.

   Also cross-links with profinite reflection were missing, and so I added them. Also cross-linked with finite set, with localic reflection and maybe with more.

   The entry profinite space is still stubby/unsatisfactory.