If I remember my Optics 201 and 202 classes correctly, object and image space don't necessarily correspond to physical spaces and can even be in the same physical space. For example, when you look in your bathroom mirror the object and image space coincide. These spaces can even extend to opposite sides of a lens. The entrance pupil for an optical system (which always occupies object space) may actually fall behind the last lens, in the physical space where the image is formed, while the exit pupil (which always occupies image space) can fall in front of the system in the physical space the object occupies.
As an example, the exit pupil of a cassegrain telescope lies behind the secondary mirror, meaning that the exit pupil is at the front of the telescope, just like the object is. Despite this, the exit pupil is still in image space, not object space.
To get more technically accurate, both image and object spaces are specific types of optical spaces and both extend to infinity in all directions. They are merely mathematical tools to help us analyze and design optical systems. Rays moving from one medium to another (air to lens) undergo a "mathematical transformation" and enter another optical space. This mathematical transformation is just terminology that means that we are performing the same mathematical operations on all of the rays, such as using the laws of refraction or reflection to find their new trajectory.