The Freudenthal Space for Approximate Systems of Compacta and Some Applications
نویسنده
چکیده
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 stablish 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).
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