Applications of the Stone-Čech compactification to free topological groups
نویسندگان
چکیده
منابع مشابه
Applications of the Stone-cech Compactification to Free Topological Groups
In this note the Stone-Cech compactification is used to produce short proofs of two theorems on the structure of free topological groups. The first is: The free topological group on any Tychonoff space X contains, as a closed subspace, a homeomorphic copy of the product space X". This is a generalization of a result of B. V. S. Thomas. The second theorem proved is C. Joiner's, Fundamental Lemma.
متن کاملAlgebra in the Stone - Čech Compactification and its Applications to Ramsey Theory
Let me begin by expressing my sincere gratitude to the Japanese Association of Mathematical Sciences for inviting me to present this lecture and for giving me the JAMS International Prize for 2003 . I am deeply honored. This lecture is not a survey, but simply a discussion of some topics that I find interesting. For the most recent surveys of this subject area in which I have participated see [...
متن کاملSubgroups of Free Topological Groups and Free Topological Products of Topological Groups
Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9]. However we might expect a subgroup theorem when a continuous Schreier transversal exists, and we give such a result in th...
متن کاملFree Boolean Topological Groups
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 specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.
متن کاملThe Stone-Čech compactification of Tychonoff spaces
A topological space X is said to be completely regular if whenever F is a nonempty closed set and x ∈ X \F , there is a continuous function f : X → [0, 1] such that f(x) = 0 and f(F ) = {1}. A completely regular space need not be Hausdorff. For example, ifX is any set with more than one point, then the trivial topology, in which the only closed sets are ∅ and X, is vacuously completely regular,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0424994-x