Abstract. The main purpose of this paper is to construct a 2-equivalent compactification X of a ray whose remainder is homeomorphic to X and such that X is a Kelley Continuum. In order to construct this example, we prove a theorem which gives conditions for an inverse limit of arcs X to be the compactification of a ray and X is a Kelley continuum.
We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.
For a given space X let C.X / be the family of all compact subsets of X . A space X is dominated by a space M if X has an M -ordered compact cover, this means that there exists a familyA space X is strongly dominated by a space M if there exists an M -ordered compact cover F such that for any compact K X there is F 2 F such that K F . Let K.X / D C.X / n f;g be the set of all nonempty compact subsets of a space X endowed with the Vietoris topology. We prove that a space X is strongly dominated by a space M if and only if K.X / is strongly dominated by M and an example is given of a -compact space X such that K.X / is not Lindelöf †. It is stablished that if the weight of a scattered compact space X is not less than c, then the spaces C p .K.X // and K.C p .X// are not Lindelöf †. We show that if X is the one-point compactification of a discrete space, then the hyperspace K.X / is semi-Eberlein compact.
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