Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T03:14:13.550Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Birkhoff, G.Lattice theory (American Math. Soc., Colloquium Publications No. 25, Second Edition, 1948).Google Scholar
(2)McCartan, S. D.On subsets of a partially ordered set. Proc. Cambridge Philos. Soc. 62 (1966), 583–595.CrossRefGoogle Scholar
(3)Wolk, E. S.Order-compatible topologies for a partially ordered set. Proc. Amer. Math. Soc. 9 (1958), 524–529.CrossRefGoogle Scholar