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On subcontinua and continuous images of \(\beta \mathbb{R} \setminus \mathbb{R}\). (English) Zbl 1393.54015

Summary: We prove that the Čech-Stone remainder of the real line has a family of \(2^{\mathfrak{c}}\) mutually non-homeomorphic subcontinua.
We also exhibit a consistent example of a first-countable continuum that is not a continuous image of \(\mathbb{H}^\ast\).

MSC:

54F15 Continua and generalizations
03E50 Continuum hypothesis and Martin’s axiom
03E65 Other set-theoretic hypotheses and axioms
54A35 Consistency and independence results in general topology
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D40 Remainders in general topology
54G20 Counterexamples in general topology
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