Reconstructing an Open Order from Its Closure, with Applications to Space-Time Physics and to Logic

Studia Logica 100 (1-2):419-435 (2012)
Abstract
In his logical papers, Leo Esakia studied corresponding ordered topological spaces and order-preserving mappings. Similar spaces and mappings appear in many other application areas such the analysis of causality in space-time. It is known that under reasonable conditions, both the topology and the original order relation $${\preccurlyeq}$$ can be uniquely reconstructed if we know the “interior” $${\prec}$$ of the order relation. It is also known that in some cases, we can uniquely reconstruct $${\prec}$$ (and hence, topology) from $${\preccurlyeq}$$. In this paper, we show that, in general, under reasonable conditions, the open order $${\prec}$$ (and hence, the corresponding topology) can be uniquely determined from its closure $${\preccurlyeq}$$
Keywords ordered topological space  order-preserving mappings  open and closed orders  space-time geometry  logic
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,404
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
E. C. Zeeman (1963). Causality Implies the Lorentz Group. Journal of Mathematical Physics 5 (4):490-493.
Citations of this work BETA

No citations found.

Similar books and articles
Peter Roeper (1997). Region-Based Topology. Journal of Philosophical Logic 26 (3):251-309.
Tim Maudlin (2010). Time, Topology and Physical Geometry. Aristotelian Society Supplementary Volume 84 (1):63-78.
Paul Bankston (1984). Expressive Power in First Order Topology. Journal of Symbolic Logic 49 (2):478-487.
Andrzej W. Jankowski (1985). Galois Structures. Studia Logica 44 (2):109 - 124.
Analytics

Monthly downloads

Added to index

2012-02-10

Total downloads

12 ( #130,321 of 1,102,977 )

Recent downloads (6 months)

5 ( #62,029 of 1,102,977 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.