topology – List of all possible unions of given sets

I’m trying to generate a list of all possible unions of some sets to generate topological space from a given basic sets.
For ex: Given {1}, {2}, {4}, {1,3}, i should get
{{}, {1}, {2}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3, 4}}.
I found the following interesting post
https://stackoverflow.com/questions/8814059/generating-topological-space-diagram-in-mathematica/8815337