Continuous mapping theorem

The continuous mapping theorem is an important rule in math. It says that if you start with something that has a certain set of properties, and you make a change to it by doing something to it, then it will still keep those same properties. For example, let's say you draw a triangle on a piece of paper. That triangle has certain properties, like its shape, size, and color. If you want to make a change to the triangle, like stretching it out or coloring it a different color, then the continuous mapping theorem says that your triangle will still have the same properties, like the new shape, size, and color. It's like when you change the way something looks, but it still keeps the same properties.