Beschreibung:
In this paper two theorems are established which are consequences of some earlier approximation results of the author. The first theorem is a controlled boundary theorem for finite-dimensional manifolds. By this we mean an ordinary boundary theorem plus small ε \varepsilon -control in a given parameter space. The second theorem is a controlled h h -cobordism theorem for finite-dimensional manifolds with small ε \varepsilon -control in a given parameter space. These results generalize the End Theorem and the Thin h h -Corbordism of Quinn.