Can anyone give me an example of compact set of which the derived set is infinitely countable set??
thks in advance, I have no idea about this .
2026-04-09 14:41:15.1775745675
Give the example of compact set with infinite countable derived set
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For example, put $A:=\{1,\frac{1}{2},\frac{1}{4},...\}$.
Then the set $B:=\{0\}\cup\bigcup_n \left(\frac{1}{2^n} + \frac{1}{2^n} A\right)$ is compact (closed and bounded) and has derived set $B'=\{0\}\cup \{\frac{1}{2},\frac{1}{4},...\}$.