Countably generated space
Imagine you have a big bag of toys, but you can only play with the toys in the bag in a certain way.
A countably generated space is like that bag of toys. It's a space, or a collection of things, that can only be created by taking a certain set of toys and combining them in a certain way.
But not just any toys can be used to create this space! The toys must be countable, which means you can put them in order and assign each one a number (like 1, 2, 3, and so on).
So, to create a countably generated space, you take your countable set of toys and use them to make a bigger collection of things. The way you put them together is important, because it has to follow certain rules in order to create this space.
In the end, you have a special kind of space that was constructed using a specific set of toys in a specific way. And like a bag of toys, you can play with this space in certain ways, depending on the rules that were used to create it.
A countably generated space is like that bag of toys. It's a space, or a collection of things, that can only be created by taking a certain set of toys and combining them in a certain way.
But not just any toys can be used to create this space! The toys must be countable, which means you can put them in order and assign each one a number (like 1, 2, 3, and so on).
So, to create a countably generated space, you take your countable set of toys and use them to make a bigger collection of things. The way you put them together is important, because it has to follow certain rules in order to create this space.
In the end, you have a special kind of space that was constructed using a specific set of toys in a specific way. And like a bag of toys, you can play with this space in certain ways, depending on the rules that were used to create it.
Related topics others have asked about: