Example 2.16

Example 2.16: Let $$X = \{a,b,c,d\}$$, and let $$T = \{\emptyset, X, \{a,b,c\}, \{a,b,d\}, \{a,b\}, \{c\} \}$$. Then $$b$$ is a limit point of the set $$\{a,c,d\}$$ because every open set that contains $$b$$ contains a point of $$\{a,c,d\}$$ different from $$b$$. On the other hand, $$c$$ is not a limit point of the set $$\{a,c,d\}$$ because there exists an open set containing $$c$$--namely, $$\{c\}$$--that contains no point in $$\{a,c,d\}$$ different from $$c$$.