Maximal metrizable remainders of locally compact spaces

Let R con be the set of classes R ( X ) of remainders of metrizable compactifications of all locally compact noncompact connected separable metrizable spaces X. Results of Chatyrko and Karassev (2013) [4] imply that R con is ordered by inclusion. For a given locally compact noncompact connected metrizable space X we construct a zero-dimensional metrizable remainder of X which contains any other zero-dimensional element of R ( X ) . As application of this we show that R con , ordered by inclusion, is isomorphic to ω 1 + 1 .