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I read this:
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?
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?