Timeline for Direct limit of Cantor sets

7 events

when toggle format	what		by	license	comment
May 4, 2018 at 9:27	answer	added	YCor		timeline score: 4
May 4, 2018 at 9:19	comment	added	YCor		Just a remark: Consider $C=A^{\omega}$, where $A$ is a finite set with $\|A\|\ge 2$, and $f_n=f$ the shift $(a_n)_{n\ge 0}\mapsto (a_{n+1})_{n\ge 0}$. Then the direct limit is the quotient of $C$ by the equivalence relation "to be eventually equal". The quotient topology is the indiscrete topology. This is not a counterexample (since it has an obvious basis of clopen subsets), but indicates that we should keep in mind that the direct limit can fail to be Hausdorff.
May 3, 2018 at 21:24	history	edited	Forever Mozart	CC BY-SA 4.0	added 75 characters in body
May 3, 2018 at 21:19	history	edited	Forever Mozart	CC BY-SA 4.0	added 12 characters in body
May 3, 2018 at 19:31	history	edited	Forever Mozart	CC BY-SA 4.0	added 223 characters in body
May 3, 2018 at 18:43	history	edited	Forever Mozart	CC BY-SA 4.0	added 1 character in body
May 3, 2018 at 18:22	history	asked	Forever Mozart	CC BY-SA 4.0