In this paper we define a space σ(X) for approximate systems of compact spaces. The construction is due to H. Freudenthal for usual inverse sequences [4, p. 153–156]. We establish the following properties of this space: (1) The space σ(X) is a paracompact space, (2) Moreover, if X is an approximate sequence of compact (metric) spaces, then σ(X) is a compact (metric) space (Lemma 2.4). We give the following applications of the space σ(X): (3) If X is an approximate system of continua, then X = limX is a continuum (Theorem 3.1), (4) If X is an approximate system of hereditarily unicoherent spaces, then X = limX is hereditarily unicoherent (Theorem 3.6), (5) If X is an approximate system of trees with monotone onto bonding mappings, then X = limX is a tree (Theorem 3.13).
@article{urn:eudml:doc:41241,
title = {The Freudenthal space for approximate systems of compacta and some applications.},
journal = {Publicacions Matem\`atiques},
volume = {39},
year = {1995},
pages = {215-232},
mrnumber = {MR1370882},
zbl = {0879.54012},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41241}
}
Loncar, Ivan. The Freudenthal space for approximate systems of compacta and some applications.. Publicacions Matemàtiques, Tome 39 (1995) pp. 215-232. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41241/