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Solution of two problems of Arhangel'skiĭ and Wiegandt

Published online by Cambridge University Press:  24 October 2008

A. J. Ward
A. J. Ward
Affiliation:
Emmanuel College, Cambridge
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Extract

In their paper (l) on the general theory of connectednesses and disconnectednesses, Arhangel'skiĭ and Wiegandt conclude by proposing several problems. We shall show in this note, by elementary constructions (assuming of course the axiom of choice), that the answer to their questions (d) and (e) is negative in both cases; we also consider a modified form of question (d) to which the answer is positive. Our notation is that of (l) and references, unless otherwise stated, are to that paper; thus ‘(1·3)’ means ‘Proposition 1·3 of (l)’, but ‘(2·1 above)’ means ‘Proposition 2·1 of the present note.’

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 61 - 64
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Abhanoel'skiĭ, A. V. and Wiegandt, R.Connectednesses and disconnectednesses in topology. General Topology and Appl. 5 (1975), 9–33.CrossRefGoogle Scholar
(2)Collins, P. J.Connection properties in topological spaces. Math. Balkanica 1 (1971), 44–51.Google Scholar