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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
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