scholarly journals Global hyperbolicity is stable in the interval topology

2011 ◽  
Vol 52 (11) ◽  
pp. 112504 ◽  
Author(s):  
J. J. Benavides Navarro ◽  
E. Minguzzi
Keyword(s):  
Global Hyperbolicity ◽  
Interval Topology

scholarly journals On Completeness of Sliced Spaces under the Alexandrov Topology

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 99
Author(s):  
Nazli Kurt ◽  
Kyriakos Papadopoulos
Keyword(s):  
Product Topology ◽  
Global Hyperbolicity ◽  
Interval Topology

We show that in a sliced spacetime ( V , g ) , global hyperbolicity in V is equivalent to T A -completeness of a slice, if and only if the product topology T P , on V, is equivalent to T A , where T A denotes the usual spacetime Alexandrov “interval” topology.

scholarly journals Fermat Metrics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1422
Author(s):  
Antonio Masiello
Keyword(s):  
Variational Methods ◽  
Morse Theory ◽  
Sagnac Effect ◽  
Variational Theory ◽  
Global Hyperbolicity ◽  
Fermat Principle ◽  
Multiple Image ◽  
Light Rays ◽  
Stationary Spacetimes

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

Quotient groups and realization of tight Riesz groups

1973 ◽  
Vol 16 (4) ◽  
pp. 416-430 ◽  
Author(s):  
John Boris Miller
Keyword(s):  
Normal Subgroup ◽  
Open Interval ◽  
Canonical Homomorphism ◽  
Interval Topology ◽  
Essential Step ◽  
Image Position ◽  
Quotient Groups

Let (G, ≼) be an l-group having a compatible tight Riesz order ≦ with open-interval topology U, and H a normal subgroup. The first part of the paper concerns the question: Under what conditions on H is the structure of (G, ≼, ∧, ∨, ≦, U) carried over satisfactorily to by the canonical homomorphism; and its answer (Theorem 8°): H should be an l-ideal of (G, ≼) closed and not open in (G, U). Such a normal subgroup is here called a tangent. An essential step is to show that ≼′ is the associated order of ≦′.

On the H -Ordered Interval Topology

1968 ◽  
Vol s1-43 (1) ◽  
pp. 517-520
Author(s):  
S. D. McCartan
Keyword(s):  
Interval Topology

scholarly journals Conical spacetimes and global hyperbolicity

2015 ◽  
Vol 45 (1) ◽  
pp. 215-229 ◽  
Author(s):  
Günther Hörmann
Keyword(s):  
Global Hyperbolicity

The new interval topology on lattice products

1970 ◽  
Vol 66 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Frieda Holley
Keyword(s):  
Interval Topology
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