Topology

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Moderate

Closures And Interiors In The Excluded Point Topology

TOPO-RU9BK4

Let $X=\{a,b,c\}$ and $\tau = \{U\subseteq X : b\notin U\}\cup\{ X\}$.

Then, $\tau$ defines a topology on $X$.

Which of the following are the closure and interior, respectively, of $A=\{b,c\}$ with respect to this topology?

A

$\{b\}$, $\{c\}$

B

$A$, $\emptyset$

C

$X$, $\emptyset$

D

$A$, $\{c\}$

E

$X$, $\{c\}$