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 کاملTopological Symmetry Groups of Small Complete Graphs
Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R. In this paper, we determine for each complete graph Kn with n ≤ 6, what groups can occur as topological symmetry groups or orientation preserving topological symmetry groups of some embedding of the graph in R.
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: Topology and its Applications
سال: 2001
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00235-7