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Topology

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Moderate

Metric Space Of Cardinality 4

TOPO-NFKTKN

Suppose that $(X,d)$ is a metric space, where the space $X$ consists of four elements (or points).

Choose ALL the correct statements from the list.

A

Every subset of $X$ is closed.

B

There exist two different points $x,y$ such that the open sets in $X$ are $\emptyset$, $X$, $\{x,y\}$ and $X\setminus \{x,y\}$.

C

There exists $c>0$ such that $d(a,b)=c$ if $a\neq b$.

D

There exists $x\in X$ such that the open sets in $X$ are $\emptyset$, $X$, $\{x\}$ and $X\setminus \{x\}$.

E

The topology on $(X,d)$ is the discrete topology.