In [5 ; 6] the author considers the following two problems posed by Professor Lloyd Tucker.

Problem 1. Does there exist a 1-dimensional continuum X without the fixed point property such that every retract of X has the fixed point property with respect to one-to-one maps?

Let L/K be a field extension of characteristic p ≠ 0. The existence of intermediate fields over which L is regular, separable, or modular is important in recent Galois theories. For instance, see [1; 2; 3; 4; 7; 8; 9 and 14].

Let K be a knot in a manifold M. Corresponding to a representation of Π1(M — K) into a transitive group of permutations there is a branched covering space of M. K is covered by which may be a link of several components. The set of linking numbers between the various components of has long been recognised as a useful knot invariant. Bankwitz and Schumann used this invariant in considering dihedral coverings of Viergeflechte.

Throughout this paper X will denote a complex Banach space and all operators T will be assumed to be continuous linear transformations from X into X. If T is an operator then ┘(T), γ(T), and R(T) will denote the spectrum of T, the spectral radius of T, and range of T, respectively. This paper contains necessary and sufficient conditions for the (norm) convergence of {Tn } when T is an operator on X.