Zeeman, in his paper 'Topology of Minkowski Space' made two conjectures :
(1) the topology in Minkowski Space that induces the 3-dimensional Euclidean topology on every space- like hyperplane (S-topology) has G as its group of homeomorphisms, where G is the smallest group generated by the inhomogeneous Lorentz group and dilatation (multiplication by +ve scalars);
(2) the topology on Minkowski space that induces the one-dimensional Euclidean topology on every time-like line (T-topology) also has G as its homeomorphism group.
Since it is known that G is precisely the set of < - automorphism (where < is the causality relation on Minkowski space), we have made an alternative formulation of the second conjecture as follows : every homeomorphism of the T-topology is a < - automorphism.
Here we have dealt with a weaker version of Zecman's conjecture on space topology.
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U. P. ; S. Choudhury, "A weaker version of zeeman's conjecture on space topology ", Journal of Ultra Scientist of Physical Sciences, Volume 21, Issue 2, Page Number 531-542, 2018Copy the following to cite this URL:
U. P. ; S. Choudhury, "A weaker version of zeeman's conjecture on space topology ", Journal of Ultra Scientist of Physical Sciences, Volume 21, Issue 2, Page Number 531-542, 2018Available from: https://www.ultrascientist.org/paper/1220/