A mirror box evokes a finite cosmos that looks endless. The box contains only three balls, yet the mirrors that line its walls produce an infinite number of images. Of course, in the real universe there is no boundary from which light can reflect. Instead a multiplicity of images could arise as light rays wrap around the universe over and over again. From the pattern of repeated images, one could deduce the universe's true size and shape.
Topology shows that a flat piece of spacetime can be folded into a torus when the edges touch.
In a similar manner, a flat strip of paper can be twisted to form a Moebius Strip . The 3D version of a moebius strip is a Klein Bottle , where spacetime is distorted so there is no inside or outside, only one surface. A simply connected Euclidean or hyperbolic universe would indeed be infinite. An observer would see multiple images of each galaxy and could easily misinterpret them as distinct galaxies in an endless space, much as a visitor to a mirrored room has the illusion of seeing a huge crowd. All possible Universes are finite since there is only a finite age and, therefore, a limiting horizon.