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A Stone-Čech compactification for limit spaces


Author: G. D. Richardson
Journal: Proc. Amer. Math. Soc. 25 (1970), 403-404
MSC: Primary 54.22
DOI: https://doi.org/10.1090/S0002-9939-1970-0256336-1
MathSciNet review: 0256336
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Abstract: O. Wyler [Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.] has given a Stone-Čech compactification for limit spaces. However, his is not necessarily an embedding. Here, it is shown that any Hausdorff limit space $ (X,\tau )$ can be embedded as a dense subspace of a compact, Hausdorff, limit space $ ({X_1},{\tau _1})$ with the following property: any continuous function from $ (X,\tau )$ into a compact, Hausdorff, regular limit space can be uniquely extended to a continuous function on $ ({X_1},{\tau _1})$.


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

  • [1] N. Bourbaki, General topology. Part I, Hermann, Paris and Addision-Wesley, Reading, Mass., 1966. MR 34 #5044a.
  • [2] H. R. Fischer, Limesräume, Math. Ann. 137 (1959), 269–303 (German). MR 0109339, https://doi.org/10.1007/BF01360965
  • [3] O. Wyler, The Stone-Čech compactification for limit spaces, Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0256336-1
Keywords: Stone-Čech compactification, limit spaces, ultrafilters
Article copyright: © Copyright 1970 American Mathematical Society