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A class T of subsets of X is called a topology on X if it satisfies these 2 conditions:

1. The union of every class of sets in T is a set in T.

2. the intersection of every finite class of sets in T is a set in T.

The sets in the class T are called the open sets of the topological space (X,T).

I'm a little confused by what open sets mean here. Do they mean that every point in the set is an interior point?

Let's say X is the metric space [tex]\mathbb{R}[/tex] with the regular metric, and I chose T to be all the closed sets in X. Then T satisfies the 2 conditions mentioned above. So T is a topology on X.

So the sets in T are closed, but I call them the open sets of the topological space (X,T)?

Can anybody help me to clarify this?

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# Confused by open sets

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