The Wallman compactification is an epireflection
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- by Douglas Harris PDF
- Proc. Amer. Math. Soc. 31 (1972), 265-267 Request permission
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
- Horst Herrlich, On the concept of reflections in general topology, Contributions to Extension Theory of Topological Structures (Proc. Sympos., Berlin, 1967) Deutscher Verlag Wissensch., Berlin, 1969, pp. 105–114. MR 0284986
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- 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
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 265-267
- DOI: https://doi.org/10.1090/S0002-9939-1972-0288731-0
- MathSciNet review: 0288731