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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-4,
author = {Benjamin Vejnar},
title = {Topological compactifications},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {233-253},
zbl = {1241.54017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-4}
}
Benjamin Vejnar. Topological compactifications. Fundamenta Mathematicae, Tome 215 (2011) pp. 233-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-3-4/