2(N0) ways of approaching a continuum with [1, infinity)

摘要

In 2014, V. Martinez-de-la-Vega and P. Minc proved that, for an arbitrary nondegenerate metric continuum X, there is an uncountable collection kappa of topologically distinct metric compactifications of [1, infinity), having X as the remainder. It is not clear without the continuum hypothesis that cardinality of kappa is go. However, the continuum hypothesis is rarely necessary in the theory of metric continua. To support this assertion, presented here is an explicit construction of a compact metric space K with 2(N0) mutually not homeomorphic components each of which is a compactification of [1, infinity), having a copy of X as the remainder. (C) 2016 Elsevier B.V. All rights reserved.