Characterizing Endpoints for a Family of Set-valued Inverse Limits
Keywords:
branch points, endpoints, inverse limits, set-valued functionsAbstract
We investigate the endpoints of inverse limits of set-valued functions using A. Lelek's definition of an endpoint. We provide two characterizations for a point to be an endpoint of the inverse limit for a family of set-valued functions. The first characterization utilizes limit points of intersections of special arcs in the inverse limit, whereas the second characterization focuses on sequences of branch points. The paper concludes with several examples demonstrating how endpoints can be identified using finite approximations of the inverse limit.
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