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We introduce the concept of proper convergence of a sequence of subspaces of a metric space and then prove that a continuum X is weakly chainable if there is a… Click to show full abstract
We introduce the concept of proper convergence of a sequence of subspaces of a metric space and then prove that a continuum X is weakly chainable if there is a sequence of arcs converging properly to it. Also, we prove that a continuum X is weakly chainable if and only if there is a sequence of arcs in the Hilbert cube converging properly to an embedded copy of X. The proof is based on an Anderson–Choquet-type theorem (valid also for set-valued functions).
Keywords:
weakly chainable;
anderson choquet;
choquet type;
type theorem
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
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Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!