Čech-Stone remainders of spaces that look like $[0,\infty)$

Alan Dow; Klaas Pieter Hart

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Čech-Stone remainders of spaces that look like $[0,\infty)$

Alan Dow·Klaas Pieter Hart

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Abstract

We show that many spaces that look like the half~line~$\halfline=[0,\infty)$ have, under~$\CH$, a Čech-Stone-remainder that is homeomorphic to~$\Hstar$. We also show that $\CH$ is equivalent to the statement that all standard subcontinua of~$\Hstar$ are homeomorphic. The proofs use Model-theoretic tools like reduced products and elementary equivalence; rather than constructing homeomorphisms we show that the spaces in question have isomorphic bases for the closed sets.

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BibTeX RIS

Alan Dow, Klaas Pieter Hart. 1993-05-18. Čech-Stone remainders of spaces that look like $[0,\infty)$. https://arxiv.org/abs/math/9305202

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