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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Wallman compactification is an epireflection


Author: Douglas Harris
Journal: Proc. Amer. Math. Soc. 31 (1972), 265-267
MathSciNet review: 0288731
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Abstract | References | Additional Information

Abstract: It is shown that a map having an extension to a closed map between the Wallman compactifications of its domain and range has a unique such extension. A consequence is that the collection of such maps forms the morphisms of a category on which the Wallman compactification is an epireflection, answering a question raised by Herrlich.


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

  • [1] Horst Herrlich, On the concept of reflections in general topology, Contributions to Extension Theory of Topological Structures (Proc. Sympos., Berlin, 1967) Deutsch. Verlag Wissensch., Berlin, 1969, pp. 105–114. MR 0284986
  • [2] John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
  • [3] V. I. Ponomarev, Extension of many-valued mappings of topological spaces to their compactifications, Mat. Sb. (N.S.) 52 (94) (1960), 847–862 (Russian). MR 0121779


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288731-0
Keywords: Wallman compactification, closed map, epireflection, maximal closed filter
Article copyright: © Copyright 1972 American Mathematical Society