Lusternik–Schnirelmann category
Lusternik-Schnirelmann category is a big, grown-up math concept that helps us understand how many paths there are between different points in a space. Imagine you're playing a game of "the floor is lava" and you need to get from your bed to your door without touching the floor.
The number of steps it takes you to get there is like the "category" of the space you're moving in. For example, if you have to take 10 different steps on the way, the category of that space is 10.
But sometimes, the path you take to get from one point to another might be more complicated. Maybe you have to go up and over a chair, climb up a bookshelf, and swing from the door handles to avoid the floor. That's where Lusternik-Schnirelmann category comes in - it tells us how many different ways there are to get from one point to another, even if those paths are really convoluted.
So next time you're hopping around your room to avoid the floor, remember that mathematicians use complicated ideas like Lusternik-Schnirelmann category to help them understand how paths work in all sorts of different spaces!
The number of steps it takes you to get there is like the "category" of the space you're moving in. For example, if you have to take 10 different steps on the way, the category of that space is 10.
But sometimes, the path you take to get from one point to another might be more complicated. Maybe you have to go up and over a chair, climb up a bookshelf, and swing from the door handles to avoid the floor. That's where Lusternik-Schnirelmann category comes in - it tells us how many different ways there are to get from one point to another, even if those paths are really convoluted.
So next time you're hopping around your room to avoid the floor, remember that mathematicians use complicated ideas like Lusternik-Schnirelmann category to help them understand how paths work in all sorts of different spaces!