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

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
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