Semi-locally simply connected
Okay kiddo, let's try to understand what "semi-locally simply connected" means in simpler terms. Imagine you have a big playground with lots of different things to play with, like a swing set, a slide, and a sandbox. Now, imagine you have a long rope that you can use to walk around the playground while holding onto it.
When we say something is "simply connected," it means that you can walk all the way around it while holding your rope without running into anything that gets in your way. But sometimes, there might be something in the playground that you can't walk around, like a big tree or a giant boulder. If that happens, the playground is not simply connected.
But if the playground is semi-locally simply connected, it means that even though there might be obstacles in the way, you can still find a way to walk around them by going a little bit out of your way. For example, you might have to walk around the tree or boulder to get to the other side of the playground, but you can still stay connected to your rope and eventually get back to where you started.
Now, let's apply this idea to math. When we talk about space in math, we use a fancy word called a "topology" to describe how things are connected. Just like our playground, we can say that a space is simply connected if you can walk all the way around it without running into any obstacles. But if there are obstacles, the space might still be semi-locally simply connected if you can find a way to go around them.
Why do we care about this in math? Well, it turns out that spaces that are semi-locally simply connected have some special properties that are really useful for studying things like geometry and physics. So even though it might sound like a complicated idea, it's actually really important and helps us understand the world around us better.
When we say something is "simply connected," it means that you can walk all the way around it while holding your rope without running into anything that gets in your way. But sometimes, there might be something in the playground that you can't walk around, like a big tree or a giant boulder. If that happens, the playground is not simply connected.
But if the playground is semi-locally simply connected, it means that even though there might be obstacles in the way, you can still find a way to walk around them by going a little bit out of your way. For example, you might have to walk around the tree or boulder to get to the other side of the playground, but you can still stay connected to your rope and eventually get back to where you started.
Now, let's apply this idea to math. When we talk about space in math, we use a fancy word called a "topology" to describe how things are connected. Just like our playground, we can say that a space is simply connected if you can walk all the way around it without running into any obstacles. But if there are obstacles, the space might still be semi-locally simply connected if you can find a way to go around them.
Why do we care about this in math? Well, it turns out that spaces that are semi-locally simply connected have some special properties that are really useful for studying things like geometry and physics. So even though it might sound like a complicated idea, it's actually really important and helps us understand the world around us better.