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Fully admissible binary relations in topology

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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Extract

A fully admissible binary relation (3) is an operator , other than the equality operator and universal operator , which assigns to each space |S, τ|, a reflexive, symmetric, binary relation , and which is such that for any continuous mapping implies . With each such relation , we associate a ‘separation axiom’ , as well as ‘-regularity’ and ‘-connectedness’, where ≡ -regularity + T0, and -regularity + -connectedness ≡ indiscreteness.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 259 - 264
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Archangel'skii, A. V. and Wiegandt, R. Connectednesses and disconnectednesses in topology. Gen. Top. and its Appl., North-Holland Publ. Co. 5 (1975), 9–33.Google Scholar
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(3)McSherry, D. M. G.A general theory of separation, regularity, and connectedness properties. Math. Proc. Cambridge Philos. Soc. 80 (1976), 81–90.CrossRefGoogle Scholar