Local boundedness

Local boundedness means that something is not too big or too small in a certain area. Think of a playground. You can run, jump, and play as much as you want, but you can't go past the gates of the playground. That's the boundary. Inside the playground, you can only move around a limited area, so you're bounded.

Now, let's apply this concept to mathematics. Imagine a graph with a bunch of points on it. If we say that a function is locally bounded, it means that the function doesn't get too big or too small in a specific area around a point on the graph. This area is called a neighborhood. So, if we focus on that neighborhood, we can see that the function stays within a certain range of values, just like how we stay within the gates of the playground.

Overall, local boundedness is a fancy math term that means something is not too big or too small in a specific area. Just like how we have to stay inside the boundaries of a playground, a function has to stay within a certain range of values in a neighborhood on a graph.