A new subcontinuum of $\beta \mathbb{R}\setminus \mathbb{R}$

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.