Let X a b c and let a b b c a c a b c Show that X is a t

Let X = {a, b, c} and let = {, {a, b}, {b, c}, {a, c}, {a, b, c}}. Show that (X, ) is a topological space.

Solution

For any element in the set t , its complement is also in the set.

X is in the set

empty set is in the set.

Union of any number of set is in the set

but intersection of {a,b} and {a,c.} is not in the set. So it must not be a toplogogical space