Dow, Alan; Hart, K. P. Čech-Stone remainders of spaces that look like \([0,\infty)\). (English) Zbl 0837.54018 Acta Univ. Carol., Math. Phys. 34, No. 2, 31-39 (1993). Summary: We show that many spaces that look like the half line \(\mathbb{H} = [0, \infty)\) have, under CH, a Čech-Stone-remainder that is homeomorphic to \(\mathbb{H}^*\). We also show that CH is equivalent to the statement that all standard subcontinua of \(\mathbb{H}^*\) are homeomorphic. The proofs use model-theoretic tools like reduced products and elementary equivalence. Cited in 3 Documents MSC: 54D40 Remainders in general topology 03E50 Continuum hypothesis and Martin’s axiom 54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites Keywords:Čech-Stone-remainder PDF BibTeX XML Cite \textit{A. Dow} and \textit{K. P. Hart}, Acta Univ. Carol., Math. Phys. 34, No. 2, 31--39 (1993; Zbl 0837.54018) Full Text: arXiv EuDML OpenURL