A & B are open and

$A\cap B\ =\ \phi\$

A and B are open

A and B are closed

E is bounded

every finite subset of E has limit point in E

E is closed

every infinite subset of E has limit point in E

for each real number n, there is an element $x_n$ such that

there is a real number k such that $\left|x\right|>k\ \forall\ x\in E$

for each real number n, $\left|x_n\right|>n\ \ \forall\ x_n\in E$

there is a real number k such that $\left|x\right|<k\ \forall\ x\in E$

every point of E is a limit point of E

every limit point of E is a point of E

every point of E is a interior point of E

every interior point of E is a point of E

every point of E is a limit point of E

every limit point of E is a point of E

every point of E is a limit point of E and every limit point of E is a point of E

every interior point of E is a point of E

Every bounded subset of $R^k$ has a limit point in $R^k$

Every infinite subset of $R^k$ has a limit point in $R^k$

Every subset of $R^k$ has a limit point in $R^k$

Every bounded infinite subset of $R^k$ has a limit point in $R^k$

If E is infinite subset of a compact set K, then E has a limit point in K.

If E is a subset of a compact set K, then E has a limit point in K.

If E is infinite subset of a compact set K, then E has a limit point in E.

If E is finite subset of a compact set K, then E has a limit point in K.

E is open X iff E is open in Y

E is closed X iff E is closed in Y

E is compact X iff E is compact in Y

All the above

$E=\overline{E}$ iff E is closed

$E=E^o$ iff E is open

$\overline{E}$ is the smallest closed set contains E

$\overline{E}$ is the largest closed set contained in E

open

closed

bounded

compact

connected

compact

perfect

closed

R

[a,b]

(a,b)

{a,b}

$E\subset E^o$

$E=E^o$

$E\supset E^o$

$E\ne E^o$

$\overline{E}\supset E$

$E=\overline{E}$

$E\supset\overline{E}$

$E\ne\overline{E}$

open ball

closed ball

open ball and closed ball

neither open ball nor closed ball