Compactifications with almost locally compact outgrowth

Rayburn, Marlon C.

doi:10.1090/S0002-9939-1989-0961408-4

Compactifications with almost locally compact outgrowth
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by Marlon C. Rayburn

Proc. Amer. Math. Soc. 106 (1989), 223-229

DOI: https://doi.org/10.1090/S0002-9939-1989-0961408-4

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Abstract:

An extension of a result of Hatzenbuhler and Mattson gives a sufficient condition that the locally compact part of an arbitrary Tichonov space has a compactification with a countably infinite outgrowth. This leads to a characterization for almost locally compact outgrowths, and some sufficient conditions for their existence. Examples are given showing the conditions are not necessary.

References

Dennis K. Burke, Closed mappings, Surveys in general topology, Academic Press, New York-London-Toronto, Ont., 1980, pp. 1–32. MR 564098
James Hatzenbuhler and Don A. Mattson, On Hausdorff compactifications of non-locally compact spaces, Internat. J. Math. Math. Sci. 2 (1979), no. 3, 481–486. MR 542961, DOI 10.1155/S0161171279000375
J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
Kenneth D. Magill Jr., Countable compactifications, Canadian J. Math. 18 (1966), 616–620. MR 198420, DOI 10.4153/CJM-1966-060-6
Marlon C. Rayburn, On Hausdorff compactifications, Pacific J. Math. 44 (1973), 707–714. MR 317277
Leo Zippin, On Semicompact Spaces, Amer. J. Math. 57 (1935), no. 2, 327–341. MR 1507076, DOI 10.2307/2371210