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

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

1993-05-18

arxiv.org/abs/math/9305202v1

Acta Univ. Carolin. Math. Phys. 34 (1993), no. 2, 31--39

Mathematics

Logic

Scientific paper

We show that many spaces that look like the half~line~$\halfline=[0,\infty)$ have, under~$\CH$, a \v{C}ech-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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