The Freudenthal space for approximate systems of compacta and some applications.

Loncar, Ivan. "The Freudenthal space for approximate systems of compacta and some applications.." Publicacions Matemàtiques 39.2 (1995): 215-232. <http://eudml.org/doc/41241>.

@article{Loncar1995,
abstract = {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).},
author = {Loncar, Ivan},
journal = {Publicacions Matemàtiques},
keywords = {Espacio topológico compacto; Espacios métricos; Espacio metrizable compacto; approximate sequence; approximate system of continua; approximate system of trees},
language = {eng},
number = {2},
pages = {215-232},
title = {The Freudenthal space for approximate systems of compacta and some applications.},
url = {http://eudml.org/doc/41241},
volume = {39},
year = {1995},
}

TY - JOUR
AU - Loncar, Ivan
TI - The Freudenthal space for approximate systems of compacta and some applications.
JO - Publicacions Matemàtiques
PY - 1995
VL - 39
IS - 2
SP - 215
EP - 232
AB - 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).
LA - eng
KW - Espacio topológico compacto; Espacios métricos; Espacio metrizable compacto; approximate sequence; approximate system of continua; approximate system of trees
UR - http://eudml.org/doc/41241
ER -