0
$\begingroup$

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

2 Answers 2

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 $E' = [0,1]$.

  • 0
    So simple. Feel bad :( – 2017-01-12
0

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

  • 0
    So if I draw Venn Diagram then $E$ is divided into $E\backslash E'$ and $E'$ because $E'$ is in $E$. But wrong? – 2017-01-12