The question is following:
Identify $\mathrm{Int}(A)$, $\mathrm{Bd}(A)$, A' and $\mathrm{Cl}(A)$ in the following cases:
(a) $X=\{a,b\}$ with the discrete topology, $A=\{a\}$.
My answer is the following:
- $\mathrm{Int}(A)= \{a\}$.
- $\mathrm{Bd}(A)=\emptyset$.
- A'= \emptyset.
- $\mathrm{Cl}(A)=\{a\}$
(b) $X=\{a,b\}$ with the trivial [indiscrete] topology, $A=\{a\}$.
My answer is the following:
- $\mathrm{Int}(A)= \emptyset$.
- $\mathrm{Bd}(A)= \emptyset$.
- A'= \{b\}.
- $\mathrm{Cl}(A)=\{a,b\}$.
Please correct my answer.