Volume 213 / 2011
Fundamenta Mathematicae 213 (2011), 233-253 MSC: Primary 54D35; Secondary 54C20. DOI: 10.4064/fm213-3-4
We study those compactifications of a space such that every autohomeomorphism of the space can be continuously extended over the compactification. These are called H-compactifications. Van Douwen proved that there are exactly three H-compactifications of the real line. We prove that there exist only two H-compactifications of Euclidean spaces of higher dimension. Next we show that there are 26 H-compactifications of a countable sum of real lines and 11 H-compactifications of a countable sum of Euclidean spaces of higher dimension. All H-compactifications of discrete and countable locally compact spaces are described.