Is the space which I see with my open eyes and closed eyes the same space? And what are the tiny dots which I see with my closed eyes?
It is probably the same space. Inner experiences can be taken into our outer life. Even the OM sound can be heard by some in daily life. Similarly the spiritual eye can be seen by some with open eyes. Divine love which one felt in meditation can be perceived also when engaging in the outer world.
Concerning the dots, many things can be seen with closed eyes: shapes, forms, images. If you are lucky, these dots are part of the vishuddha chakra (throat chakra), which, when one sees it, is according to Yogananda “a smoke color, with little specks of light.”
All the best,