Piecewise algebraic space
Alright kiddo, imagine you have a bunch of math equations that look different depending on which numbers you use. Let's make it simple and say you have one equation for when you have a number less than or equal to 5, and a different equation for when you have a number greater than 5.
Now imagine taking both of those equations and putting them on the same graph, but only showing the parts of each equation that apply to certain numbers. So for the first equation, you would show the part of the graph where x (that's the number we're using) is less than or equal to 5. And for the second equation, you would show the part where x is greater than 5.
That's basically what a piecewise algebraic space is. It's a way to graph different equations on the same space, but only showing certain parts of each equation that apply to certain numbers. It's like having a map of different cities, but only showing the parts of each city that are important for the map you're making. Make sense, kiddo?
Now imagine taking both of those equations and putting them on the same graph, but only showing the parts of each equation that apply to certain numbers. So for the first equation, you would show the part of the graph where x (that's the number we're using) is less than or equal to 5. And for the second equation, you would show the part where x is greater than 5.
That's basically what a piecewise algebraic space is. It's a way to graph different equations on the same space, but only showing certain parts of each equation that apply to certain numbers. It's like having a map of different cities, but only showing the parts of each city that are important for the map you're making. Make sense, kiddo?