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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0288731-0
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] H. Herrlich, On the concept of reflections in general topology, Proc. First Internat. Sympos. on Extension Theory of Topological Structures, VEB Deutscher Verlag Wissenschaften, Berlin, 1969. MR 0284986 (44:2210)
  • [2] J. L. Kelley, General topology, Van Nostrand, Princeton, N.J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [3] V. I. Ponomarev, On the extension of multivalued mappings of topological spaces to their compactifications, Mat. Sb. 52 (94) (1960), 847-862; English transl., Amer. Math. Soc. Transl. (2) 38 (1964), 141-158. MR 22 #12513. MR 0121779 (22:12513)


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

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