TOPOLOGY, COSMOLOGY AND THE SHAPE OF SPACE
5. Topology
Under certain of the 2-dimensional models of the universe, it is possible
to see yourself.
For example, in the spherical model, if you look far
enough in any direction,
then you will see the back of your own head!
If you inhabit a conical universe, then there would be
one special
direction in which you look and see the back of your own head. In all
other directions, your line of sight would spiral off to infinity.
The difference in these line-of-sight self images reflect the different
topologies of these different surfaces.
Here are some objects which are topologically equivalent and some which are
not:
We can ask "What
are the topological properties of the universe?"
Goto Section 6.