Warped products of metric spaces of curvature bounded from above

In this work we extend the idea of warped products, which was previously defined on smooth Riemannian manifolds, to geodesic metric spaces and prove the analogue of the theorems on spaces with curvature bounded from above.Suppose that function $f\ :\ M\to R\sp{+}$ is continuous and ($M\times\sb{f}\ N,\ d)$ denotes the warped product of two metric spaces $(M,\ d\sb{M})$ and $(N,\ d\sb{N})$. We prove the following main results in this thesis.Theorem. If $(M,\ d\sb{M})$ and $(N,\ d\sb{N})$ are geodesic metric spaces and if $(M\times\sb{f}\ N,\ d)$ has nonpositive curvature, then (1) $(M,\ d\sb{M})$ has nonpositive curvature. (2) $(N,\ d\sb{N})$ has nonpositive curvature if f has a minimum. (3) f is convex.Theorem. Let M be R or a graph. If $(N,\ d\sb{N})$ has nonpositive curvature and $f\ :\ M\to R\sp{+}$ is convex then $(M\times\sb{f}\ N,\ d)$ has nonpositive curvature.U of I OnlyETDs are only available to UIUC Users without author permissio