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On normal subspaces

Published online by Cambridge University Press:  17 April 2009

D.B. Gauld ,
I.L. Reilly  and
M.K. Vamanamurthy
D.B. Gauld
Affiliation:
Department of Mathematics, University of Auckland, Private Bag, Auckland, New Zealand.
I.L. Reilly
Affiliation:
Department of Mathematics, University of Auckland, Private Bag, Auckland, New Zealand.
M.K. Vamanamurthy
Affiliation:
Department of Mathematics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

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In this paper the anti-normal property is studied. A space is anti-normal if its only normal subspaces are those whose cardinalities require them to be normal. It is shown that every topological space of at least four elements contains a normal three point subspace from which it follows that there is only one non-trivial anti-normal space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1981 , pp. 1 - 4
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Bankston, Paul, “The total negation of a topological property”, Illinois J. Math. 23 (1979), 241–252.CrossRefGoogle Scholar
[2]Reilly, I.L. and Vamanamurthy, M.K., “Some topological anti-properties”, Illinois J. Math. (to appear).Google Scholar