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Order-continuous functions and order-connected spaces

Published online by Cambridge University Press:  24 October 2008

D. C. J. Burgess  and
S. D. McCartan
D. C. J. Burgess
Affiliation:
Queen's University, Belfast
S. D. McCartan
Affiliation:
Queen's University, Belfast
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Extract

We introduce and compare four procedures for defining the order-continuity of a function from one topological ordered space into another, where each reduces to the usual conception when the orderings of the two spaces are trivial. Chiefly for the purposes of this comparison, we use the idea of an ‘order-connected’ space, and in the course of investigating under which types of order-continuous functions this property is preserved, we are helped in assessing their relative importance.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 27 - 31
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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