Results 251 to 260 of about 289,513 (282)

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
openaire   +1 more source

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
openaire   +3 more sources

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
openaire   +1 more source

FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES

Mathematics of the USSR-Izvestiya, 1991
See the review in Zbl 0722.22001.
openaire   +1 more source

Free subgroups of free abelian topological groups

Mathematical Proceedings of the Cambridge Philosophical Society, 1986
In this paper we prove a theorem which gives general conditions under which the free abelian topological group F(Y) on a space Y can be embedded in the free abeian topological group F(X) on a space X.
Katz, E., Morris, S. A., Nickolas, P.
openaire   +2 more sources

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.
Ribes, Luis, Zalesskii, Pavel
openaire   +1 more source

Topological Free Group-Groupoids

Journal of Interdisciplinary Mathematics
In this work, we introduced some new properties on topological group-groupoid and topological free group-groupoid. We obtain some results related to topological group-groupoid and topological free group-groupoid. In the end of this study, we get results written as propositions. Between the quantity y demand and the price.
openaire   +1 more source

Free Topological Groups over (Semi) Group Actions

Annals of the New York Academy of Sciences, 1996
ABSTRACTWe study equivariant embeddability into G‐groups. A new regionally proximal type relation introduced in the paper gives a necessary condition providing some counter‐examples. We establish also some sufficient conditions (for locally compact acting semigroups G, for instance) improving results of M.Eisenberg and J. de Vries.
openaire   +1 more source

Norms on Free Topological Groups

Bulletin of the London Mathematical Society, 1978
Bicknell, Kevin, Morris, Sidney A.
openaire   +2 more sources

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 \(\Phi x = \varphi x\) \((x\in X)\).
openaire   +2 more sources