# Least upper bound

1. Jul 14, 2009

### symbol0

I read the following:
"If {$$T_i$$} is a non empty family of topologies on our set X, then the least upper bound of this family is precisely the topology generated by the class $$\bigcup T_i$$; that is, the class $$\bigcup T_i$$ is an open subbase for the least upper bound of the family {$$T_i$$} ."

I understand that the least upper bound L of a family of topologies is the intersection of all topologies which are stronger than each $$T_i$$ but I don't understand why $$\bigcup T_i$$ is a subbase for L.

2. Jul 15, 2009

### g_edgar

Then you should work on the proof of that.