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1989•Proceedings of the American Mathematical SocietyOpen access

Compactifications with almost locally compact outgrowth

Marlon C. Rayburn

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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.

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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.

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Available 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.

Key concepts: Compactification (mathematics), Locally compact space, Extension (predicate logic), Mathematics, Compact space, Pure mathematics, Compact disc, Space (punctuation)

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