Partition of a set in a metric space

Question

Why $$ E=(E\backslash E')\cup E' $$ isn't true in general? I don't see. $\text{Thank you very much}$.

score 2 · Accepted Answer · answered Jan 12 '17 at 07:39

2

Because that would assume $E' \subset E$, which isn't always true. Consider $\Bbb R$ with the usual topology and $E = (0,1)$. Then $E' = [0,1]$.

answered Jan 12 '17 at 07:39

score 0 · Answer 2 · answered Jan 12 '17 at 07:37

0

Hint: Draw a Venn Diagram (then it will also be clear under which conditions that assertion holds)

answered Jan 12 '17 at 07:37

b00n heT

So if I draw Venn Diagram then $E$ is divided into $E\backslash E'$ and $E'$ because $E'$ is in $E$. But wrong? – NeedForHelp Jan 12 '17 at 07:38

2 Answers2