# Ordered topological vector space

Imagine you have a special kind of space where you can put numbers and arrows (vectors). Let's call it an "ordered topological vector space" because it has a special way of organizing things.

First, let's talk about the "ordered" part. This means you can put these numbers in order from smallest to biggest, like counting from 1 to 10. And you can also put the arrows in order based on their length, from small to big.

Now, let's talk about the "topological" part. This means there are special rules about how things can move around in the space. For example, if you take a point (let's call it A) and move it closer to another point (let's call it B), then there must be a way to smoothly move A along a path to get to B. You can't just make a big jump or move in a weird way.

Finally, let's talk about the "vector" part. This means the arrows can be added together and multiplied by numbers, just like in math class. You can also "scale" the arrows by stretching or shrinking them.

So, when you put all of these things together, you get an "ordered topological vector space." It's a special kind of space where you can put numbers and arrows, organize them in order, move them around smoothly, and do math with the arrows.