A note on Wallman extendible functions
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- by Darrell W. Hajek PDF
- Proc. Amer. Math. Soc. 44 (1974), 505-506 Request permission
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
- R. Engelking, Outline of general topology, North-Holland Publishing Co., Amsterdam; PWN—Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. Translated from the Polish by K. Sieklucki. MR 0230273 Hajek, A characterization of ${T_3}$ spaces, Indiana Univ. Math. J. 23 (1973), 23-25.
- Henry Wallman, Lattices and topological spaces, Ann. of Math. (2) 39 (1938), no. 1, 112–126. MR 1503392, DOI 10.2307/1968717
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 505-506
- MSC: Primary 54D35; Secondary 54C20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0345073-4
- MathSciNet review: 0345073