Topological Groups and Generalized Manifolds
نویسنده
چکیده
The terminology used in the statement of this theorem, and in what follows, is that of our two previous papers on generalized manifolds [l, 2] , and we assume that the reader is familiar with them. We make, however, one change. We find it convenient to define infinite cycles in the following way: We add to G an ideal point, g, taking as neighborhoods of g those open subsets of G whose closures are not compact. Then G+ — G\Jg+ is compact. Now an infinite cycle of G is defined to be a relative cycle of G mod g+. That this definition of infinite cycles is equivalent to the one used in [2] follows from Theorem 1.1 of [2].
منابع مشابه
PRECOMPACT TOPOLOGICAL GENERALIZED GROUPS
In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.
متن کاملNEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES
The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces and tangent spaces of Lie groups, separately.
متن کاملω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS
Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...
متن کاملOn some generalized recurrent manifolds
The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds, called, super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [A.A. Shaikh and A. Patra, On a generalized class of recurrent manifolds, Arch. Math. (Brno) 46 (2010) 71--78.] and weakly generalized recurrent manifolds ...
متن کاملGeneralized Neuwirth Groups and Seifert Fibered Manifolds
The topological properties of the generalized Neuwirth groups are discussed. For example, we shall demonstrate that the group ? k n is the fundamental group of the Seifert bered space | {z } n times): Moreover we discuss some other invariants and algebraic properties of the above groups.
متن کاملEmbeddings of Homology Manifolds in Codimension
Among the many problems attendant to the discovery of exotic generalized manifolds [2, 3] is the \normal bundle" problem, that is, the classi cation of neighborhoods of generalized manifolds tamely embedded in generalized manifolds (with the disjoint disks property). In this paper we study the normal structure of tame embeddings of a closed generalized manifold X into topological manifolds V n+...
متن کامل