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Locally convex syntopogenous spaces

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 Stranmillis College, Belfast
M. Fitzpatrick
Affiliation:
Queen's University of Belfast and Stranmillis College, Belfast
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Extract

In (1) the authors introduced the idea of a syntopogenous pre-ordered space and, in (2), discussed the more general notion of a convex syntopogenous space. The former generalizes Nachbin's ‘uniform preordered space’ (4) and Singal and Lal's ‘proximity preordered space’ (7); the latter does the same for Nachbin's ‘convex topological space’ (4) and Redfield's ‘nearly uniform ordered space’ (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 445 - 448
Copyright
Copyright © Cambridge Philosophical Society 1979

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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)Burgess, D. C. J. and Fitzpatrick, M.Syntopogenous preordered spaces (II). Math. Proc. Cambridge Philos. Soc. 83, (1978), 19–24.CrossRefGoogle Scholar
(3)Császár, A.Foundations of general topology (Oxford, Pergamon Press, 1963).Google Scholar
(4)Nachbin, L.Topology and order (Princeton, Van Nostrand, 1965).Google Scholar
(5)Redfield, R. H.Ordering uniform completions of partially ordered sets, Canad. J. Math. 26, (1974), 644–664.CrossRefGoogle Scholar
(6)Redpield, R. H.Uniformly convex totally ordered sets. Proc. Amer. Math. Soc. 51, (1975), 289–294.CrossRefGoogle Scholar
(7)Singal, M. K. and Sunder, Lal.Proximity ordered spaces. J. London Math. Soc. (2), 14, (1976), 393–40CrossRefGoogle Scholar