Clopen set
Imagine you have a special box that has a door. If the door is completely closed, we call it a "closed" box. If the door is completely open, we call it an "open" box.
Now, what if the door is partly closed and partly open? It's neither completely closed nor completely open, right? This is called a "clopen" box.
In math, a "clopen set" works the same way. A set of numbers can be "open" if it doesn't include its boundaries (like a partially open door), "closed" if it does include its boundaries (like a completely closed door), or "clopen" if it includes some boundaries but not others (like a partly closed door).
So, a "clopen set" is a special kind of set that is neither completely open nor completely closed, but somewhere in between.
Now, what if the door is partly closed and partly open? It's neither completely closed nor completely open, right? This is called a "clopen" box.
In math, a "clopen set" works the same way. A set of numbers can be "open" if it doesn't include its boundaries (like a partially open door), "closed" if it does include its boundaries (like a completely closed door), or "clopen" if it includes some boundaries but not others (like a partly closed door).
So, a "clopen set" is a special kind of set that is neither completely open nor completely closed, but somewhere in between.