Research on "Classification of filters and subsets of reals with respect to selector, and convergence properties of hyperspacea"

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We investigate topological properties of spaces which admit continuous (weak)selction and also the relationship between topological properties of hyperspaces and that of base spaces, especially convergence properties. The main results obtained by our project are as follows ;(1)If X is homogeneous space, then countable (pseudo) compactness of hyperspace implies that of countable product of X. This gives a partial solution of Ginsburgs problem.(2)We establishe that topologically welorderability of base space is equivalent to the existence of Fell continuous selection.(3)There exists a space which admit a continuous weal selection but small inductive dimension can be taken any natural number.