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Syntopogenous preordered spaces (II)

Published online by Cambridge University Press:  24 October 2008

D. C. J. Burgess  and
M. Fitzpatrick
D. C. J. Burgess
Affiliation:
Queen's University of Belfast and Northern Ireland Polytechnic, Jordanstown
M. Fitzpatrick
Affiliation:
Queen's University of Belfast and Northern Ireland Polytechnic, Jordanstown
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Extract

In (1) the authors introduced the idea of a syntopogenous preordered space (SPS), thereby generalizing simultaneously the concepts of ‘uniform preordered space’ and ‘proximity preordered space’. In the case of a classical topology the SPS condition was seen to be equivalent to the condition, ‘convex plus T1-preordered’. In the present paper we show that, in the general case, the SPS condition may be characterized as the sum of two generalizations of the logically independent conditions of convexity and T1-preorderedness.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 1 , January 1978 , pp. 19 - 24
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1) Burgess, D. C. J. and Fitzpatrick, M. Syntopogenous preordered spaces. Math. Proc. Cambridge Philos. Soc. 80 (1976), 71–79.CrossRefGoogle Scholar
(2) Császár, A. Foundations of general topology (Oxford: Pergamon Press, 1963).Google Scholar
(3) McCartan, S. D. Separation axioms for topological ordered spaces. Proc. Cambridge Philos. Soc. 64 (1968), 965–973.CrossRefGoogle Scholar
(4) Nachbin, L. Topology and order (Princeton, New Jersey: D. Van Nostrand Company, Inc., 1965).Google Scholar
(5) Redfield, R. H. Ordering uniform completions of partially ordered sets. Canad. J. Math. 26 (1974), 644–664.CrossRefGoogle Scholar
(6) Redfield, R. H. Uniformly convex totally ordered sets. Proc. Amer. Math. Soc. 51 (1975), 289–294.CrossRefGoogle Scholar