A weaker version of zeeman's conjecture on space topology 

Author & Affiliation:
Ujagar Patel
Department of Mathematics, Government Autonomous College, Bhawanipatna (INDIA)
Somanath Choudhury
Department of Mathematics, Government Autonomous College, Bhawanipatna (INDIA)
Keyword:
weaker , version, conjecture on space topologyu00a0
Issue Date:
August 2009
Abstract:

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.

Pages:
531-542
ISSN:
2319-8044 (Online) - 2231-346X (Print)
Source:
DOI:
jusps-A
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Copy the following to cite this article:

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, 2018

Copy 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, 2018

Available from: https://www.ultrascientist.org/paper/1220/

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