Tame surfaces and tame subsets of spheres in $E\sp{3}$

Locally Tame Curves and Surfaces in Three-dimensional Manifolds

Tame Flows

The tame flows are “nice” flows on “nice” spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow Φ : R×X → X on pfaffian set X is tame if the graph of Φ is a pfaffian subset of R×X×X . Any compact tame set admits plenty tame flows. We prove that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric ...

Tame structures

We study various notions of “tameness” for definably complete expansions of ordered fields. We mainly study structures with locally o-minimal open core, d-minimal structures, and dense pairs of d-minimal structures.

Tame Triods in 3-space

A triod is a homeomorphic image of the set consisting of three linear intervals which are disjoint except for a single point which is an end point of each interval. The images of the intervals are called branches of the triod and their intersection the branch point. In [3 ] the author presented an example of a wild triod in euclidean 3-space, E3, which has an open 3-cell complement in compactif...

Tame Mappings Are Semismooth

Superlinear convergence of the Newton method for nonsmooth equations requires a “semismoothness” assumption. In this work we prove that locally Lipschitz functions definable in an o-minimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth. Semialgebraic, or more generally, globally subanalytic mappings present the special interest of being γ-order semismo...