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

Publicacions Matemàtiques (1995)

- Volume: 39, Issue: 2, page 215-232
- ISSN: 0214-1493

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topLoncar, 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 -

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