  We investigate the global spacetime structure of torus de Sitter universe,
which is exact de Sitter space with torus identification based on the flat
chart. We show that past incomplete null geodesics in torus de Sitter universe
are locally extendible. Then we give an extension of torus de Sitter universe
so that at least one of the past incomplete null geodesics in the original
spacetime becomes complete. However we find that extended torus de Sitter
universe has two ill behaviors. The first one is a closed causal curve. The
second one is so called quasi regular singularity, which means that there is no
global, consistent extension of spacetime where all curves become complete,
nevertheless each curve is locally extensible.
