Existence and uniqueness theorems for extensions of zero-dimensional compact metric spaces
R. S.
Pierce
1-21
A general theorem on the convergence of operator semigroups
Thomas G.
Kurtz
23-32
An infinite-dimensional Schoenflies theorem
D. E.
Sanderson
33-39
On Milnor's invariant for links. II. The Chen group
Kunio
Murasugi
41-61
Collaring and $(n-1)$-manifold in an $n$-manifold
C. L.
Seebeck
63-68
Topological semigroups with invariant means in the convex hull of multiplicative means
Anthony To-ming
Lau
69-84
Embedding as a double commutator in a type I $AW\sp{\ast} $-algebra
Herbert
Halpern
85-98
Boundaries of semilinear spaces and semialgebras
R. E.
Worth
99-119
Isotopisms of semigroups of functions
Kenneth D.
Magill
121-128
A characterization of unitary duality
David W.
Roeder
129-135
Abstract: The concept of unitary duality for topological groups was introduced by H. Chu. All mapping spaces are given the compact-open topology. Let G and H be locally compact groups. ${G^ \times }$ is the space of continuous finite-dimensional unitary representations of G. Let ${\operatorname{Hom}}({G^ \times },{H^ \times })$ denote the space of all continuous maps from ${G^ \times }$ to $ {H^ \times }$ which preserve degree, direct sum, tensor product and equivalence. We prove that if H satisfies unitary duality, then $ {\operatorname{Hom}}(G,H)$ and $ {\operatorname{Hom}}{\mkern 1mu} ({H^ \times },{G^ \times })$ are naturally homeomorphic. Conversely, if $ {\operatorname{Hom}}(Z,H)$ and $ {\operatorname{Hom}}{\mkern 1mu} ({H^ \times },{Z^ \times })$ are homeomorphic by the natural map, where Z denotes the integers, then H satisfies unitary duality. In different contexts, results similar to the first half of this theorem have been obtained by Suzuki and by Ernest. The proof relies heavily on another result in this paper which gives an explicit characterization of the topology on $ {\operatorname{Hom}}{\mkern 1mu} ({G^ \times },{H^ \times })$. In addition, we give another necessary condition for locally compact groups to satisfy unitary duality and use this condition to present an example of a maximally almost periodic discrete group which does not satisfy unitary duality.
Infinite deficiency in Fr\'echet manifolds
T. A.
Chapman
137-146
Abstract: Denote the countable infinite product of lines by s, let X be a separable metric manifold modeled on s, and let K be a closed subset of X having Property Z in X, i.e. for each nonnull, homotopically trivial, open subset U of X, it is true that $ U\backslash K$ is nonnull and homotopically trivial. We prove that there is a homeomorphism h of X onto $X \times s$ such that $h(K)$ projects onto a single point in each of infinitely many different coordinate directions in s. Using this we prove that there is an embedding of X as an open subset of s such that K is carried onto a closed subset of s having Property Z in s. We also establish stronger versions of these results.
Banach spaces of Lipschitz functions and vector-valued Lipschitz functions
J. A.
Johnson
147-169
The module index and invertible ideals
David W.
Ballew
171-184
Abstract: A. Fröhlich used the module index to classify the projective modules of an order in a finite dimensional commutative separable algebra over the quotient field of a Dedekind domain. This paper extends Fröhlich's results and classifies the invertible ideals of an order in a noncommutatives eparable algebra. Several properties of invertible ideals are considered, and examples are given.
Quasiconformal mappings and Schwarz's lemma
Peter J.
Kiernan
185-197
Abstract: In this paper, K quasiconformal maps of Riemann surfaces are investigated. A theorem, which is similar to Schwarz's lemma, is proved for a certain class of K quasiconformal maps. This result is then used to give elementary proofs of theorems concerning K quasiconformal maps. These include Schottky's lemma, Liouville's theorem, and the big Picard theorem. Some of Huber's results on analytic self-mappings of Riemann surfaces are also generalized to the K quasiconformal case. Finally, as an application of the Schwarz type theorem, a geometric proof of a special case of Moser's theorem is given.
Approximation by polynomials subordinate to a univalent function
Thomas H.
MacGregor
199-209
L\'evy measures for a class of Markov semigroups in one dimension
Ken iti
Sato
211-231
Abstract: Given a Markov semigroup of linear operators in the space of realvalued continuous functions on the line vanishing at infinity, we prove that the Lévy measure exists if the domain of the infinitesimal generator contains $ \mathcal{D}_K(D_m D_s^+)$, the domain of William Feller's generalized second order differential operator restricted to functions with compact supports. We give estimate of singularity of the Lévy measure and representation of the infinitesimal generator. Conversely, given Lévy measure or the form of infinitesimal generator, existence of the corresponding Markov semigroup is shown under some conditions. The case of circles is also discussed.
An asymptotic property of Gaussian processes. I
Hisao
Watanabe
233-248
The Blaschke condition for bounded holomorphic functions
Pak Soong
Chee
249-263
Countable paracompactness and weak normality properties
John
Mack
265-272
Nonlinear evolution equations and product integration in Banach spaces.
G. F.
Webb
273-282
Abstract: The method of product integration is used to obtain solutions to the nonlinear evolution equation $g' = Ag$ where A is a function from a Banach space S to itself and g is a continuously differentiable function from $ [0,\infty )$ to S. The conditions required on A are that A is dissipative on S, the range of $(e - \varepsilon A) = S$ for all $\varepsilon \geqq 0$, and A is continuous on S.
Stable maps and Schwartz maps
Andre
de Korvin
283-291
The Freudenthal-Springer-Tits constructions revisited
Kevin
McCrimmon
293-314