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On separation axioms for certain types of ordered topological space

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

An ordered topological space (E, τ, ≥) is a set E endowed with a topology τ and a partial order ≥. For such a space order separation axioms have been studied by Nachbin (6) and McCartan (3). In this paper we discuss the consequences for these axioms of the imposition, in turn, of four conditions on (E, τ, ≥), namely convexity (6), continuity, anticontinuity and bicontinuity (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 1 , July 1977 , pp. 59 - 65
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Burgess, D. C. J.Analytical Topology (London, D. Van Nostrand Company, Ltd., 1966).Google Scholar
(2)Gillman, L. and Jerison, M.Rings of continuous functions (Princeton, D. Van Nostrand Company, Inc., 1960).CrossRefGoogle Scholar
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(6)Nachbin, L.Topology and order (Princeton, D. Van Nostrand Company, Inc., 1965).Google Scholar