- E8
[0SG]Prerequisites:[0PJ], [0PQ], [0GJ], [0Q8].Difficulty:**.
Find a subset A of \(ℝ\) such that the following 7 subsets of \(ℝ\) are all distinct:
\[ A,~ ~ \overline A,~ ~ {{A}^\circ } ,~ ~ {{\left(\overline A\right)}^\circ },~ ~ \overline{\left({{A}^\circ }\right)} ,~ ~ \overline{\left({{\left(\overline A\right)}^\circ }\right)},~ ~ {{\left(\overline{\left({{A}^\circ }\right)}\right)}^\circ } ~ ~ . \]Also prove that no other different sets can be created by continuing in the same way (also replacing \(ℝ\) with a generic metric space).
Solution 1
EDB — 0SG
View
English
Authors:
"Mennucci , Andrea C. G."
.
Managing blob in: Multiple languages