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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Wallman extendible functions


Author: Darrell W. Hajek
Journal: Proc. Amer. Math. Soc. 44 (1974), 505-506
MSC: Primary 54D35; Secondary 54C20
MathSciNet review: 0345073
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Abstract: It is known that any continuous function into a $ {T_4}$ space has a unique continuous Wallman extension, and that any continuous Wallman extension of a continuous function with a $ {T_3}$ range must be unique. We show that for any $ {T_3}$ space $ Y$ which is not $ {T_4}$ there exists a $ {T_3}$ space $ X$ and a continuous function $ f:X \to Y$ which has no continuous Wallman extension.


References [Enhancements On Off] (What's this?)

  • [1] R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. MR 0230273 (37 #5836)
  • [2] Hajek, A characterization of $ {T_3}$ spaces, Indiana Univ. Math. J. 23 (1973), 23-25.
  • [3] Henry Wallman, Lattices and topological spaces, Ann. of Math. (2) 39 (1938), no. 1, 112–126. MR 1503392, http://dx.doi.org/10.2307/1968717

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0345073-4
PII: S 0002-9939(1974)0345073-4
Keywords: Wallman extension, Wallman extendible function, WO-function
Article copyright: © Copyright 1974 American Mathematical Society