Hausdorff measures on abstract spaces
M.
Sion;
R. C.
Willmott
275-309
Compactification and duality of topological groups
Hsin
Chu
310-324
Finite topological spaces
R. E.
Stong
325-340
Bol loops
D. A.
Robinson
341-354
Tame surfaces and tame subsets of spheres in $E\sp{3}$
L. D.
Loveland
355-368
Elastic-plasitc torsion of a square bar
Tsuan Wu
Ting
369-401
Limit theorems for semi-Markov processes
James
Yackel
402-424
The level curves of harmonic functions
Leopold
Flatto;
Donald J.
Newman;
Harold S.
Shapiro
425-436
Dilations on invertible spaces
Ellard
Nunnally
437-448
Abstract: This paper primarily concerns certain groups of homeomorphisms which are associated in a natural way with a variety of spaces, which satisfy a set of axiomatic conditions put forth in §1. Let us suppose that $X$ is a space of the type in question and that $G$ is an appropriate group of homeomorphisms of $ X$ onto itself. In §2 we demonstrate the existence of a nonvoid subcollection $ \mathcal{D}$, the ``topological dilations,'' of $G$ which is characterized in Theorem 1 in the following fashion: suppose $f \in \mathcal{D}$ and $g \in G$, then $ g \in \mathcal{D}$ if and only if $f$ is a $G$-conjugate of $g$, that is if and only if there exists an element $ h$ of $G$ such that $f = hg{h^{ - 1}}$. We proceed then to show in §3 that if $f$ and $g$ are nonidentity elements of $G$, then we may find $\delta ,r \in G$ such that the product $(rg{r^{ - 1}})(\delta f{\delta ^{ - 1}}) \in \mathcal{D}$. We then combine this fact with the characterization of $ \mathcal{D}$ mentioned above to conclude that each element of $\mathcal{D}$ is a ``universal'' element of $ G$ in the sense that if $d \in \mathcal{D}$, then any element $g$ of $G$ may be represented as the product of two $ G$-conjugates of $ d$. Furthermore we conclude that if $g$ is not the identity element of $G$, then $g$ can be represented as the product of three $ G$-conjugates of any nonidentity element of $G$. Finally, we apply the conclusions to groups of homeomorphisms of certain spaces: for example spheres, cells, the Cantor set, etc.
Decay at infinity of solutions to partial differential equations with constant coefficients
Walter
Littman
449-459
Decomposable chainable continua
J. B.
Fugate
460-468
Regular minimal sets. I
Joseph
Auslander
469-479
Unknotting in $M\sp{2}\times I$
E. M.
Brown
480-505
Polynomial automorphic forms and nondiscontinuous groups
Marvin Isadore
Knopp
506-520
Singular perturbations on the infinite interval
Frank Charles
Hoppensteadt
521-535
On Witt's theorem in the denumerably infinite case
Herbert
Gross
536-547
Errata to ``Szeg\"o functions on a locally compact Abelian group with ordered dual''
I. I.
Hirschman
548