خاصيت كلي براي كمان ها

In this thesis, we study the notion of the {property of Kelley by arcs} for continua. The material presented here is mainly based on the recent paper of Tirado, López, an‎d Suárez López (2024), an‎d the thesis provides a detailed exposition, clarification, an‎d systematic development of their results together with additional explanations an‎d illustrative examples. After introducing the necessary background on continua, arcs, an‎d hyperspaces, we define the property of Kelley by arcs using the Hausdorff metric on the hyperspace of arcs an‎d analyze its basic features. Roughly speaking, this property describes the stability of arcs under pointwise convergence. Following the aforementioned reference, we investigate this property in several important classes of continua. We show that among finite graphs, the property of Kelley by arcs holds precisely for arcs an‎d simple closed curves. Moreover, for arc continua, this property is equivalent to the classical property of Kelley. We also characterize dendroids with this property an‎d prove that, within this class, only arcs satisfy it. Finally, we study the behavior of the property in compactifications of the ray [0,infty) an‎d present examples of spaces that satisfy the property.

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مصطفي عين اله زاده , سجاد لكزيان