For a set $A \subset \mathbb { R }$, denote by $\operatorname { Cl } ( A )$ the closure of $A$, and by $\operatorname { Int } ( A )$ the interior of $A$. There is a set $A \subset \mathbb { R }$ such that (a) $A , Cl ( A )$, and $\operatorname { Int } ( A )$ are pairwise distinct; (b) $A , Cl ( A ) , \operatorname { Int } ( A )$, and $\operatorname { Cl } ( \operatorname { Int } ( A ) )$ are pairwise distinct; (c) $A , \operatorname { Cl } ( A ) , \operatorname { Int } ( A )$, and $\operatorname { Int } ( \operatorname { Cl } ( A ) )$ are pairwise distinct; (d) $A , Cl ( A ) , \operatorname { Int } ( A ) , \operatorname { Int } ( Cl ( A ) )$, and $\operatorname { Cl } ( \operatorname { Int } ( A ) )$ are pairwise distinct.
For a set $A \subset \mathbb { R }$, denote by $\operatorname { Cl } ( A )$ the closure of $A$, and by $\operatorname { Int } ( A )$ the interior of $A$. There is a set $A \subset \mathbb { R }$ such that\\
(a) $A , Cl ( A )$, and $\operatorname { Int } ( A )$ are pairwise distinct;\\
(b) $A , Cl ( A ) , \operatorname { Int } ( A )$, and $\operatorname { Cl } ( \operatorname { Int } ( A ) )$ are pairwise distinct;\\
(c) $A , \operatorname { Cl } ( A ) , \operatorname { Int } ( A )$, and $\operatorname { Int } ( \operatorname { Cl } ( A ) )$ are pairwise distinct;\\
(d) $A , Cl ( A ) , \operatorname { Int } ( A ) , \operatorname { Int } ( Cl ( A ) )$, and $\operatorname { Cl } ( \operatorname { Int } ( A ) )$ are pairwise distinct.