Topological compactifications

Benjamin Vejnar¹

¹ Department of Mathematical Analysis Charles University 18675 Praha, Czech Republic

Fundamenta Mathematicae, Tome 213 (2011) no. 3, pp. 233-253

Résumé

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.

Détail

DOI : 10.4064/fm213-3-4

Keywords: study those compactifications space every autohomeomorphism space continuously extended compactification these called h compactifications van douwen proved there exactly three h compactifications real line prove there exist only h compactifications euclidean spaces higher dimension there h compactifications countable sum real lines h compactifications countable sum euclidean spaces higher dimension h compactifications discrete countable locally compact spaces described