A new subcontinuum of 𝛽ℝ\ℝ

Dow, Alan; Hart, Klaas

doi:10.1090/S0002-9939-97-04055-0

A new subcontinuum of $\beta \mathbb {R}\backslash \mathbb {R}$
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by Alan Dow and Klaas Pieter Hart PDF

Proc. Amer. Math. Soc. 125 (1997), 1861-1871 Request permission

Abstract:

We present a method for describing all indecomposable subcontinua of $\beta \mathbb {R}\setminus \mathbb {R}$. This method enables us to construct in $\mathsf {ZFC}$ a new subcontinuum of $\beta \mathbb {R}\setminus \mathbb {R}$. We also show that the nontrivial layers of standard subcontinua can be described by our method. This allows us to construct a layer with a proper dense $F_\sigma$-subset and bring the number of (known) nonhomeomorphic subcontinua of $\beta \mathbb {R}\setminus \mathbb {R}$ to 14.

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