Computability, corse topology and the dimensions of metric spaces

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The main topics of the project are the following: (1) The applications of topological method to the theory of the computability and domain theory; and (2) the dimensions of metric spaces and its applications. (1) An early study on the Martin topology on the domain of the formal balls of a metric space suggested an importance of the Sorgenfrey-type topologies on the real line. We investigated several Sorgenfrey-type topologies, and we have a condition that a such topology is homeomorphic to the Sorgenfrey topology. We also have a test subspace of the Khalimski space for determining the n-dimensionality of its subspaces. (2) We obtained Hurewicz formulas for large inductive dimensions on normal spaces with additional conditins. We also have a result on the transfinite separation dimension of a subspace of the Hilbert cube, and investigated an approach which unifies several small inductive dimensions of spaces including the Menger-Uryshon dimension ind and the separation dimension t.