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A general theory of separation, regularity, and connectedness properties

Published online by Cambridge University Press:  24 October 2008

D. M. G. McSherry
D. M. G. McSherry
Affiliation:
Queen's University, Belfast
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Abstract

The notion of basic topological binary relations is introduced, and corresponding to each such relation we define -regularity, -connectedness, and a separation axiom . The family of separation axioms so obtained is shown to include all the standard axioms T0, T1, …, T5, while familiar properties such as hyperconnectedness and ultraconnectedness are among the class of connectedness conditions. The regularity conditions include R0, R1, and regularity itself.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 81 - 90
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)McSherry, D. M. G.On separation axioms weaker than T1. Proc. Roy. Irish Acad. 74 (1974), 115–118.Google Scholar
(2)Stone, M. H.Applications of Boolean Algebras to Topology. Mat. Sb. (1936), 765–771.Google Scholar
(3)Wilansky, A.Between T l and T 2. Amer. Math. Monthly 74 (1967), 261–266.Google Scholar