On free actions, minimal flows, and a problem by Ellis
V Pestov - Transactions of the American Mathematical Society, 1998 - ams.org
We exhibit natural classes of Polish topological groups $ G $ such that every continuous
action of $ G $ on a compact space has a fixed point, and observe that every group with this …
action of $ G $ on a compact space has a fixed point, and observe that every group with this …
Free topological groups and the projective dimension of a locally compact abelian group
J Mack, SA Morris, ET Ordman - Proceedings of the American Mathematical …, 1973 - ams.org
It is shown that a free topological group on a ${k_\omega} $-space is a ${k_\omega} $-
space. Using this it is proved that if $ X $ is a ${k_\omega} $-group then it is a quotient of a …
space. Using this it is proved that if $ X $ is a ${k_\omega} $-group then it is a quotient of a …
Some topics in topological algebra
MM Choban - Topology and its Applications, 1993 - Elsevier
In this paper we investigate the topological structure of free topological universal algebras
with given continuous signature. We establish some properties of compact subsets of free …
with given continuous signature. We establish some properties of compact subsets of free …
Varieties of linear topological spaces
J Diestel, SA Morris, SA Saxon - Transactions of the American Mathematical …, 1972 - ams.org
This paper initiates the formal study of those classes of locally convex spaces which are
closed under the taking of arbitrary subspaces, separated quotients, cartesian products and …
closed under the taking of arbitrary subspaces, separated quotients, cartesian products and …
Imbeddings into topological groups preserving dimensions
DB Shakhmatov - Topology and its Applications, 1990 - Elsevier
We give a negative answer to the following question of Bel'nov: Can every Tychonoff space
X be imbedded as a subspace of a topological group G so that dim G⩽ dim X? We show that …
X be imbedded as a subspace of a topological group G so that dim G⩽ dim X? We show that …
Varieties of topological algebras
W Taylor - Journal of the Australian Mathematical Society, 1977 - cambridge.org
By a variety of topological algebras we mean a class V of topological algebras of a fixed type
closed under the formation of subalgebras, products and quotients (ie images under …
closed under the formation of subalgebras, products and quotients (ie images under …
[PDF][PDF] Varieties of topological groups a survey
SA Morris - Colloquium Mathematicum, 1982 - infona.pl
1. Varieties of groups. The study of varieties of groups (more generally, varieties of algebras)
has its roots in the work of Birkhoff [4] and Neumann [60] in the 1930's. A variety of groups …
has its roots in the work of Birkhoff [4] and Neumann [60] in the 1930's. A variety of groups …
Free products of topological groups
SA Morris - Bulletin of the Australian Mathematical Society, 1971 - cambridge.org
In this note the notion of a free topological product Gα of a set {Gα} of topological groups is
introduced. It is shown that it always exists, is unique and is algebraically isomorphic to the …
introduced. It is shown that it always exists, is unique and is algebraically isomorphic to the …
Free Boolean topological groups
O Sipacheva - Axioms, 2015 - mdpi.com
Known and new results on free Boolean topological groups are collected. An account of the
properties that these groups share with free or free Abelian topological groups and …
properties that these groups share with free or free Abelian topological groups and …
Free topological groups and dimension
C Joiner - Transactions of the American Mathematical Society, 1976 - ams.org
For a completely regular space X we denote by $ F (X) $ and $ A (X) $ the free topological
group of X and the free Abelian topological group of X, respectively, in the sense of Markov …
group of X and the free Abelian topological group of X, respectively, in the sense of Markov …