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$C^{0}$-space-times; causal maps; causality conditions; K-causality.

Using K-causal relation introduced by Sorkin and Woolgar [1], we generalize results of Garcia-Parrado and Senovilla [2,3] on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. $C^{0}$-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.

Sujatha Janardhan¹ R V Saraykar²

1. Department of Mathematics, St. Francis De Sales College, Nagpur 440 006, India
2. Department of Mathematics, R.T.M. Nagpur University, Nagpur 440 033, India

Published

April 2008

Manuscript received

3 January 2007

Manuscript revised

29 November 2007

Accepted

5 December 2007