Čech-Stone remainders of spaces that look like \([0,\infty)\). (English) Zbl 0837.54018

Dow, Alan; Hart, K. P.

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.

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