Further Considerations on the Separating Topology for the Space--Times of General Relativity

摘要

The separating topology S studied in an earlier report is reexamined. Using methods and ideas in papers by Goebel, Hawking, King and McCarthy a new class of topologies (Ssub(nm)) is introduced. The topology Ssub(nm) is the finest which induces Euclidean topology on timelike Csup(n)- and spacelike Csup(m)-curves. It is shown that S sub 00 =S sub 10 =S sub 01 =S sub 11 =S. A relation between (Ssub(nm)) and some topologies studied by Goebel is derived. For an arbitrary spacetime the group of S-homeomorphisms is shown to be the smooth conformal diffeomorphism group. The restriction to strongly causal spacetimes employed in the former report is no longer necessary. The question of whether S is the coarsest of comparable topologies having this homeomorphism group, is finally considered. (Atomindex citation 09:374573)