It is also proved that if X is a non-metric continuum such thatĭim(X)<∞ and such that X has the cone = hyperspace property, then X is ageneralized arc, a generalized circle, or an indecomposable continuum such that each nondegenerate proper subcontinuum of X is a generalized arc. Due to a resurgence of automated spam bots.
Hyperspaces infection full#
See our section on Problems such as a full transcription of The Houston Problem Book, and follow our Twitter. Please create an account and contribute to the Wiki. Cantor Set Approximations and Dimension Commutations in Hyperspaces. Welcome to the Hyperspace Wiki This wiki is for people who study Hyperspaces, Continuum Theory, and, more generally, Topology. In this paper we shall prove, using the inverse systems and limits, that if X is a non-metric rim-metrizable continuum and C(X) is a finite-dimensional Cartesian product, then X is a generalized arc or a generalized circle. Infection, mutation, and cancer evolution. The first step toward topologizing 2X is defining a metric H on 2X in. in the hyperspaces of the compact subsets of the original basic spaces. When these collections are topologized, they are called hyperspaces of X. Multiple Periodic Solutions of a within-host Malaria Infection Model with Time. To define the various topologies on the collection of closed subsets of a space X, certain collection of sets are considered. Let C(X) be the hyperspace of all subcontinua of a metric continuum X.Īlejandro Illanes has proved that C(X) is a finite-dimensional Cartesian product if and only if X is an arc or a circle. All spaces are assumed to be Hausdorff topological spaces. Lončar, "Hyperspaces which are products or cones", Mathematical Communications, vol.6, br. 'Hyperspaces which are products or cones', Mathematical Communications, 6(2), str.
"Hyperspaces which are products or cones." Mathematical Communications 6, br.
"Hyperspaces which are products or cones." Mathematical Communications, vol. Mathematical Communications, 6 (2), 199-215.
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