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We define the Hausdorff metric. We prove that the hyperspaces \(2^{X}\) , \(C_{n}(X)\) and \(F_{n}(X)\) are continua. We prove the existence of Whitney mappings defined on hyperspaces. We prove the existence of order arcs and its use for proving that some hyperspaces are arcwise connected. We introduce Whitney levels.

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Hyperspaces of Continua

  • 章节

  • 发表日期：

    2025年

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  • Alejandro Illanes

摘要

We define the Hausdorff metric. We prove that the hyperspaces \(2^{X}\) , \(C_{n}(X)\) and \(F_{n}(X)\) are continua. We prove the existence of Whitney mappings defined on hyperspaces. We prove the existence of order arcs and its use for proving that some hyperspaces are arcwise connected. We introduce Whitney levels.