Locally simply connected space
Okay, so imagine you have a big map of your neighborhood. You might notice that some streets only have one way in and one way out, while other streets have lots of different ways to get in and out.
In math, we call a space "locally simply connected" if it's like the streets with lots of ways in and out - you can get from one point to another by following a path (or road) that doesn't have any twists or turns that get in the way.
So if you're standing at one point in a locally simply connected space and you want to get to another point, you can always find a path that's straight and doesn't have any dead ends or loops.
It's like trying to find your way through your neighborhood without getting lost or turned around, because you know there are always lots of ways to get where you need to go.
In math, we call a space "locally simply connected" if it's like the streets with lots of ways in and out - you can get from one point to another by following a path (or road) that doesn't have any twists or turns that get in the way.
So if you're standing at one point in a locally simply connected space and you want to get to another point, you can always find a path that's straight and doesn't have any dead ends or loops.
It's like trying to find your way through your neighborhood without getting lost or turned around, because you know there are always lots of ways to get where you need to go.