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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.

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    What does A' mean? What does "phi" mean? If it means the empty set, then how does it differ from "none"?2011-10-23
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    "phi" I'm guessing is meant to be $\emptyset$ (since $\phi$ looks sometimes like an empty set). $A'$ would be the derived set: the set of all limit points).2011-10-23

1 Answers 1