Localization of a topological space
Localization of a topological space means you take a space and make it smaller by only focusing on certain parts of it. Just like when you look at a big picture but only pay attention to one part of it.
To do this, you need something called an open set. An open set is like a special box that contains a point and all the other points that are really close to it. Think of it like a big hug around a point!
When you localize a space, you pick a special point and only look at the parts of the space that are really close to that point, as if they were hugging it. You take away all the parts of the space that are too far away from that point.
This can help make a big space simpler to study. It’s like zooming in on a map to see a smaller area in detail. And just like how a map can be zoomed out again, you can also go back to looking at the whole space if you want to.
To do this, you need something called an open set. An open set is like a special box that contains a point and all the other points that are really close to it. Think of it like a big hug around a point!
When you localize a space, you pick a special point and only look at the parts of the space that are really close to that point, as if they were hugging it. You take away all the parts of the space that are too far away from that point.
This can help make a big space simpler to study. It’s like zooming in on a map to see a smaller area in detail. And just like how a map can be zoomed out again, you can also go back to looking at the whole space if you want to.
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