Let G be a compact Lie group and M be a compact G-manifold. We investigate the class of equivariant diffeomorphisms of M covering the identity map on the orbit space M/G.

We give a simple proof of the result that if the total space of a holomorphic fiber bundle is (complete) hyperbolic then both the fiber and the base manifold must be (complete) hyperbolic. Shoshichi Kobayashi tried to set up examples where the total space is hyperbolic but the base is not; our theorem shows that any such example is bound to fail.

Nearlattices, or lower semllattices in which any two elements have a supremum whenever they are bounded above, provide an interesting generalization of lattices. In this context, we study standard, neutral, and central elements, as well as standard ideals. A new perspective is obtained in the well established case of lattices.

In 1978 Almkvist and Fossum examined the decomposition of the exterior powers of basis modules in the modular representation algebra of a cyclic group of prime order. In particular they developed an isomorphism between these exterior powers and terms of binomial coefficient type in the algebra.

We derive several recurrence relations for these terms.

Since the author's article “A unified treatment of transfinite constructions …”, in Volume 22 (198O) of this Bulletin, had an encyclopaedic goal, he now takes the opportunity to answer two further questions raised since that article was submitted. The lesser of these asks whether the only pointed endofunctors for which every action is an isomorphism are the well-pointed ones, at least when the endofunctor is cocontinuous; a counter-example provides a negative answer. The more important question concerns the reflexion from the comma-category T/A into the category of algebras for the pointed endofunctor T of A, and the algebra-reflexion sequence which converges to this reflexion; and asks for simplified descriptions in the special case where T is cocontinuous. We give closed formulas in this case, both for the reflexion and for the sequence which converges to it. The reader may wonder why we care about the approximating sequence when we have a closed formula for the reflexion; the answer is that, in certain applications, we need to separate the roles of finite colimits and filtered ones.

An LCA group G is called largely open if every large subgroup (that is, subgroup of finite index) of G is open. G is power-open if the continuous endomorphism, g → ng, g ∈ G, takes open sets of G onto open sets of G for every integer n > 1.

In [2], it was asserted in Theorem 3 that the measure M(x0 + … + xx) is asymptotically , where c was an explicit constant. The value of c given was incorrect, and should be e-½γ where γ is Euler's constant. This was pointed out by the first author. In fact

where we have tried to make amends by improving the error term.