Abstract
We present several applications of the set function \(\mathcal {T}\). We start with properties of continuously irreducible metric continua and their hyperspace of subcontinua and continuously type A′ metric θ-continua. We give sufficient conditions for the noncontractibility of continua. We study strict point \(\mathcal {T}\)-asymmetry of arc-smooth metric continua and dendroids. We consider R-continua in dendroids. We give a couple of characterizations of local connectedness. We present sufficient conditions for a closed subset of a continuum to have its image under \(\mathcal {T}\) to be a shore set in the continuum. We consider generalized inverse limits of nonaposyndetic metric homogeneous continua X using the set function \(\mathcal {T}|{ }_{\mathcal {F}_1(X)}\) as an upper semicontinuous bonding function. We present more relationships between the set functions \(\mathcal {T}\) and \(\mathcal {K}\).
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Macías, S. (2021). Applications. In: Set Function T. Developments in Mathematics, vol 67. Springer, Cham. https://doi.org/10.1007/978-3-030-65081-0_7
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DOI: https://doi.org/10.1007/978-3-030-65081-0_7
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