The Freudenthal space for approximate systems of compacta

In this paper we define the Freudenthal space for approximate systems of compact spaces. The original construction due to Freudenthal was done for inverse sequences. We prove that our construction gives a paracompact space, which, in the case of an approximate sequence, is compact metric. The result is applied to approximate systems of continua and of hereditarily unicoherent continua, giving that the limit space is a continuum or a hereditarily unicoherent continuum, respectively.