A space Y is called a free space if for each compactum X the set of maps with hereditarily indecomposable fibers is a dense -subset of C(X,Y), the space of all continuous functions of X to Y. Levin proved that the interval I and the real line ℝ are free. Krasinkiewicz independently proved that each n-dimensional manifold M (n ≥ 1) is free and the product of any space with a free space is free. He also raised a number of questions about the extent of the class of free spaces. In this paper we will...
The space of Kähler metrics in a fixed Kähler class on a projective Kähler manifold is an infinite dimensional symmetric space whose geodesics are solutions of a homogeneous complex Monge-Ampère equation in , where is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials of may be approximated in a weak sense by geodesics of the finite dimensional symmetric space of Bergman metrics of height . In this article we prove that in in the case of...
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