منابع مشابه
Free 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 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 کاملOn Universal Mappings and Free Topological Groups
It has been observed that constructions so apparently different as Kronecker products, extension of the ring of operators of a module, field of quotients of an integral domain, free groups, free topological groups, completion of a uniform space, Cech compactification enter in the same frame. We intend in this paper to explain a rather general process of construction which may be applied to most...
متن کاملOn the Existence of Free Topological Groups
Given a Tychonoff space X and classes U and V of topological groups, we say that a topological group G = G(X, U, V) is a free (U, V)-group over X if (a) X is a subspace of G, (b) GE U, and (c) every continuous f:X+ H with H EV extends uniquely to a continuous homomorphism _?: G + H. For certain classes U and V, we consider the question of the existence of free (U, V)groups. Our principal result...
متن کاملFréchet-urysohn Spaces in Free Topological Groups
Let F (X) and A(X) be respectively the free topological group and the free Abelian topological group on a Tychonoff space X. For every natural number n we denote by Fn(X) (An(X)) the subset of F (X) (A(X)) consisting of all words of reduced length ≤ n. It is well known that if a space X is not discrete, then neither F (X) nor A(X) is Fréchet-Urysohn, and hence first countable. On the other hand...
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ژورنال
عنوان ژورنال: General Topology and its Applications
سال: 1975
ISSN: 0016-660X
DOI: 10.1016/0016-660x(75)90021-5