Product topology in the hyperspace of subcontinua

✍ Scribed by Alejandro Illanes; Verónica Martı́nez-de-la-Vega

• Book ID: 104295648
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 134 KB
• Volume: 105
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00065-6

✦ Synopsis

Let X be a metric continuum. Let C(X) be the hyperespace of subcontinua of X. Given two finite subsets P and Q of X, let U(P , Q) = {A ∈ C(X): P ⊂ A and A ∩ Q = ∅}. In this paper we consider C(X) with the topology τ P which have the sets U(P , Q) as a basis. In this paper we show that, for a dendroid X, some topological properties of X are very closely related to the topological structure of (C(X), τ P ).