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
Abstract: It is known that any continuous function into a space has a unique continuous Wallman extension, and that any continuous Wallman extension of a continuous function with a range must be unique. We show that for any space which is not there exists a space and a continuous function which has no continuous Wallman extension.
-  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
-  Hajek, A characterization of 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, https://doi.org/10.2307/1968717
- R. Engelking, Outline of general topology, PWN, Warsaw, 1965; English transl., North-Holland, Amsterdam; Interscience, New York, 1968. MR 36 #4508; 37 #5836. MR 0230273 (37:5836)
- Hajek, A characterization of spaces, Indiana Univ. Math. J. 23 (1973), 23-25.
- H. Wallman, Lattices and topological spaces, Ann. of Math. 89 (1938), 112-126. MR 1503392
Keywords: Wallman extension, Wallman extendible function, WO-function
Article copyright: © Copyright 1974 American Mathematical Society