I'm new to topology, and I came across this definition on topology:
Given a topological space (X, T), a topology is defined to be a collection of open subsets which satisfies the following properties: 1. empty and X are in T 2. union of arbitrary collection of sets in T are open 3. intersection of a finite number of sets in T are open.
I'm quite confused if the only sets to be considered open are the ones in T, or some of the other subsets not in T can also be considered open. Can anyone give me light to this?
Also, are all sets in T are considered to be open and closed at the same time?