Quasi-complete space

Imagine you have a big toy box full of different toys. But not all of the toys are the same. Some are bigger or smaller than others, some are soft and some are hard, and so on.

Now imagine you want to sort all of the toys in the box. But you don't just want to sort them by size or material or color. You want to sort them by something called "closeness". This means that you want to group together the toys that are similar to each other and put them in the same place. For example, all the soft toys would be in one group and all the hard toys would be in another group.

But there's a problem. Some of the toys are so different from each other that you can't group them together with any other toy. They're like the odd ones out.

This is similar to what happens with spaces in math. A "quasi-complete space" is a type of mathematical space that is like our toy box. Each point in the space is like a different toy in the box. And the "closeness" between points is like the similarity between toys.

But just like our toy box has odd toys that don't fit with any other toy, a quasi-complete space has points that can't be grouped with any other point based on their closeness. These points are called "isolated points", and they're like the odd toys in our toy box.

So, to summarize: a quasi-complete space is a mathematical space where points are grouped together based on their closeness, but there are some points that can't be grouped with any other point. These points are called "isolated points", and they're like the odd toys in a toy box.