Surjection of Fréchet spaces
Okay kiddo, let me explain what surjection of Fréchet spaces means. First, we need to know what a Fréchet space is. A Fréchet space is a fancy math term for a type of space where we can measure distances between points.
Think of a Fréchet space like a bunch of dots on a piece of paper. Each dot is called a point and we can measure how far apart two points are by drawing a line between them. Fréchet spaces are a way to talk about these types of spaces in math.
Now, surjection is another fancy math term. It means that we can map every point in one space to a corresponding point in another space. So, for example, let's say you have two pieces of paper with dots on them. And you can draw a line from every dot on the first paper to a corresponding dot on the second paper. That means you have a surjection between the two papers.
So, putting it all together, when we say there is a surjection between two Fréchet spaces, it means we can map every point in one space to a corresponding point in the other space, while still being able to measure the distance between them using the Fréchet metric.
It's kind of like connecting two dots on two different pieces of paper with a line and making sure that the length of the line doesn't change even when you move the papers around. That's what a surjection of Fréchet spaces is all about!
Think of a Fréchet space like a bunch of dots on a piece of paper. Each dot is called a point and we can measure how far apart two points are by drawing a line between them. Fréchet spaces are a way to talk about these types of spaces in math.
Now, surjection is another fancy math term. It means that we can map every point in one space to a corresponding point in another space. So, for example, let's say you have two pieces of paper with dots on them. And you can draw a line from every dot on the first paper to a corresponding dot on the second paper. That means you have a surjection between the two papers.
So, putting it all together, when we say there is a surjection between two Fréchet spaces, it means we can map every point in one space to a corresponding point in the other space, while still being able to measure the distance between them using the Fréchet metric.
It's kind of like connecting two dots on two different pieces of paper with a line and making sure that the length of the line doesn't change even when you move the papers around. That's what a surjection of Fréchet spaces is all about!