Almost open map

Imagine you have a big book with lots of maps in it and you want to color all the places that you have been to. You have some crayons of different colors like red, green and blue. But, instead of coloring all the places you have been to, you only color some of them.

Now, let's imagine that the places you colored are called "open" places and the places you did not color are called "closed" places. An almost open map is a special type of map where most of the places are open, but there might be a few places that are closed.

In math, this concept is used to describe a function that has mostly open sets as its image, with only a few closed sets. So, an almost open map is a function that maps most points from one set to another without interruption, but there might be some points that don't get mapped at all.

Think of it like a taxi driver who can take you to almost any destination, but there might be a few places she can't go to because of road closures or construction. An almost open map is similar in that it can take you almost anywhere, but there might be a few destinations that are off-limits.