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The order on the light cone and its induced topology

Kyriakos Papadopoulos

http://orcid.org/0000-0003-1042-6016

Department of Mathematics, Kuwait University, P. O. Box 5969, Safat 13060, Kuwait

E-mail Address: kyriakos.papadopoulos1981@gmail.com

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Santanu Acharjee

Department of Mathematics, Debraj Roy College, India

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, and

Basil K. Papadopoulos

Department of Civil Engineering, Democritus University of Thrace, Greece

Corresponding author.

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https://doi.org/10.1142/S021988781850069XCited by:5 (Source: Crossref)

Abstract

In this paper, we first correct a recent misconception about a topology that was suggested by Zeeman as a possible alternative to his fine topology. This misconception appeared while trying to establish the causality in the ambient boundary-ambient space cosmological model. We then show that this topology is actually the intersection topology (in the sense of Reed [The intersection topology w.r.t. the real line and the countable ordinals, Trans. Am. Math. Soc.297(2) (1986) 509–520]) between the Euclidean topology on $ℝ^{4}$ and the order topology whose order, namely horismos, is defined on the light cone and we show that the order topology from horismos belongs to the class of Zeeman topologies. These results accelerate the need for a deeper and more systematic study of the global topological properties of spacetime manifolds.

Keywords:

AMSC: 83–XX, 83F05, 85A40, 54–XX

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