Exercise 2.3

Exercise 2.3: Let $$X = \{1,2,3\}$$ and let $$T = \{ \emptyset, \{1,2,3\}, \{1\}, \{2\}, \{2,3\} \}$$. Show that $$T$$ is NOT a topology on $$X$$.

Ian_mi
$$\{1\},\{2\} \in T$$ but $$ \{1\} \cup \{2\} = \{1,2\} \notin T$$ so $$ (X,T)$$ is not a topological space.

Ian mi 20:58, March 14, 2011 (UTC)Ian_mi

'''Yes. --Steven.clontz 04:33, March 15, 2011 (UTC)'''