Abstrakt
We study those compactifications of a space such that every autohomeomorphism of the given 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 countable sum of real lines and 11 H-compactifications of countable sum of Euclidean spaces of higher dimension. All H-compactifications of discrete and countable locally compact spaces are described.