Results 81 to 90 of about 212 (106)

Proper Pseudocompact Subgroups of Pseudocompact Abelian Groups

Annals of the New York Academy of Sciences, 1994
ABSTRACT: We prove among other things that if G is a pseudocompact Abelian topological group such that |G| > c or ω1≤w(G)≤ c then G has a proper dense pseudocompact subgroup.
W W Comfort, Jan Van Mill
exaly   +2 more sources

Selectively pseudocompact groups and p-compactness

Topology and its Applications, 2020
A space \(X\) is \textit{selectively pseudocompact} if for each sequence \((U_n)_ ...
Garcia-Ferreira, S., Tomita, A. H.
openaire   +2 more sources

Continuity of the Inverse in Pseudocompact Paratopological Groups

Algebra Colloquium, 2007
By a celebrated theorem of Numakura, a Hausdorff compact topological semigroup with two-sided cancellation is a group which has inverse continuous, i.e., it is a topological group. We improve Numakura's Theorem in the realm of non-Hausdorff topological semigroups.
Romaguera, S., Sanchis, M.
openaire   +2 more sources

Continuous Selections and Locally Pseudocompact Groups

Set-Valued Analysis, 2004
Soit \(G\) un groupe topologique (localement) précompact, et soit \(\hat G\) son complété de Weil. Convenons qu'un sous-ensemble \(A\) de \(G\) est borné si toute fonction réelle continue sur \(G\) est bornée sur \(A\). Pour un ouvert précompact \(U\) de \(G\), l'auteur caractérise la propriété d'être borné en termes de sélections continues de ...
openaire   +1 more source

Pseudocompact topological groups and their properties

Siberian Mathematical Journal, 1989
A subspace X of a topological space Y is said to be bounded in Y if every continuous, real-valued function on Y is bounded on X. Using the elegant observation that a necessary and sufficient condition for boundedness of X in Y is that only finitely many elements of any locally finite family of sets open in Y can intersect X, it is shown that the ...
openaire   +1 more source

Boundedness and pseudocompactness in topological groups

Mathematical Notes of the Academy of Sciences of the USSR, 1987
Translation from Mat. Zametki 41, No.3, 400-405 (Russian) (1987; Zbl 0622.22001).
openaire   +2 more sources

Pseudocompact Topological Groups

2018
Topological groups constitute a very special subclass of topological spaces. Every topological group satisfying the \(T_0\) separation axiom is automatically Tychonoff, which means that in the class of topological groups, the axioms of separation \(T_0\), \(T_1\), \(T_2\), \(T_3\) and \(T_{3.5}\) are all equivalent.
openaire   +1 more source

Pseudocompact groups without converging sequences

Mathematical Notes of the Academy of Sciences of the USSR, 1985
Is it true that there is a nontrivial convergent sequence of elements in any pseudocompact group of weight \(\tau
Malykhin, V. I., Shapiro, L. B.
openaire   +1 more source

Pseudocompact topologies on groups

1992
This paper is a summary of results that appeared in preprint form [Dept. Math. Stat. York Univ., July 1991 (preprint \#91-19)]. They establish classes of infinite groups that admit a pseudocompact topology. A partial list is i) free groups and free Abelian groups, ii) torsion free Abelian groups, iii) torsion Abelian groups and iv) divisible Abelian ...
DIKRANJAN, Dikran, Shakhmatov D.
openaire   +2 more sources

Pseudocompactness, Measurability, and Category in Compact Groups

Annals of the New York Academy of Sciences, 1992
It is shown that in the case where G is a compact topological group satisfying certain standard cardinality conditions, a theorem of Wilcox implies that it is possible to partition G into a collection of dense subsets, whose cardinality is Card(G), where each subset is pseudocompact.
openaire   +1 more source