Results 251 to 260 of about 291,341 (280)

The Topology of Free Products of Topological Groups

1974
In [3], Graev introduced the free product of Hausdorff topological groups G and H (denoted in this paper by G ╨ H) and showed it is algebraically the free product G * H and is Hausdorff. While it has been studied subsequently, for example [4, 6, 7, 8, 11, 12], many questions about its topology remain unsolved.
Sidney A. Morris, Edward T. Ordman, H. B. Thompson   +2 more
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Free Subgroups of Free Topological Groups

1974
It is well known that every subgroup of a free group is a free group. However, it is not true in general that a subgroup of a free topological group is a free topological group.
David C. Hunt, Sidney A. Morris
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PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS

International Journal of Algebra and Computation, 2004
Let [Formula: see text] be a nonempty class of finite groups closed under taking subgroups, quotients and extensions. We consider groups G endowed with their pro-[Formula: see text] topology, and say that G is 2-subgroup separable if whenever H and K are finitely generated closed subgroups of G, then the subset HK is closed.
Luis Ribes, Pavel Zalesskii
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FREE ABELIAN TOPOLOGICAL GROUPS ON SPHERES

The Quarterly Journal of Mathematics, 1984
If X is a completely regular topological space, then the abelian topological group F(X) is a (Markov) free abelian topological group on X if X is a subspace of F(X), X generates F(X) algebraically and for every continuous mapping \(\phi\) of X into any abelian topological group G there exists a continuous homomorphism \(\Phi\) of F(X) into G that ...
Katz, Eli, Morris, Sidney A., Nickolas, Peter   +2 more
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Separable Quotients of Free Topological Groups

Canadian Mathematical Bulletin, 2019
AbstractWe study the following problem: For which Tychonoff spaces $X$ do the free topological group $F(X)$ and the free abelian topological group $A(X)$ admit a quotient homomorphism onto a separable and nontrivial (i.e., not finitely generated) group? The existence of the required quotient homomorphisms is established for several important classes of
Leiderman, Arkady, Tkachenko, Mikhail
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Free Topological Groups

2008
In this chapter, we introduce the notion of a free topological group and familiarize the reader with basic properties of these groups that will be used in the rest of the book. Free topological groups were introduced in 1941 by A. A. Markov in [305] with the clear idea of extending the well-known construction of a free group from group theory to ...
Alexander Arhangel’skii, Mikhail Tkachenko   +1 more
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FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES

Mathematics of the USSR-Izvestiya, 1991
See the review in Zbl 0722.22001.
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Norms on Free Topological Groups

Bulletin of the London Mathematical Society, 1978
Bicknell, Kevin, Morris, Sidney A.
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On free topological groups

1941
gruppe von \(G\) ist. Zu jedem vollstandig regulären \(X\) gibt es eine topologisehe Gruppe \(F\) so, daß \(X\) Teilraum von \(F\) ist und \(F\) erzeugt, und daß zu jeder Abbildung \(\varphi\) von \(X\) in eine topologische Gruppe \(G\) ein stetiger Homomorphismus \(\Phi\) von \(F\) in \(G\) existiert mit \(\Phi x = \varphi x\) \((x\in X)\).
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On the topology of the character variety of a free group

2011
Summary: We investigate the topology of the space of characters of a free group into \(\text{SL}_2\mathbb{R}\), \(\text{SL}_2\mathbb{C}\), \(\text{SO}_2\), and \(\text{SU}_2\).
Bratholdt, Stuart, Cooper, Daryl
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