Subbasis for a Topology on a Set
The trade off where we stopped at in previous page is that with simplicity in definition, comes complexity in calculation. Let’s see how.
Let X be a set. A collection of subsets of X is called a subbasis for a topology on X if the union of sets in is the whole of X.
Interesting! But how to find a topology from it?
Topology generated by a subbasis is the collection of all possible union of finite intersection of sets in .
Clearly, union of all elements in .
That’s just one of many examples, try generating more yourself!
We’ve had plenty enough examples – but are they enough? The next post (when posted) will be about many more interesting examples of topological spaces! Watch out Facebook Page/LinkedIn page for more details!