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

Título inglés The Freudenthal space for approximate systems of compacta and some applications.
Título español El espacio de Freudenthal para sistemas aproximados de compactos y algunas aplicaciones.
Autor/es Loncar, Ivan
Organización Fak. Organiz. Inform., Varazdin, Croacia
Revista 0214-1493
Publicación 1995, 39 (2): 215-232, 17 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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).
Clasificación UNESCO 121001
Palabras clave español Espacio topológico compacto ; Espacios métricos ; Espacio metrizable compacto
Código MathReviews MR1370882
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