scholarly journals Countably compact group topologies on non-torsion Abelian groups of size continuum with non-trivial convergent sequences

2019 ◽  
Vol 267 ◽  
pp. 106894
Author(s):  
Matheus Koveroff Bellini ◽  
Ana Carolina Boero ◽  
Irene Castro-Pereira ◽  
Vinicius de Oliveira Rodrigues ◽  
Artur Hideyuki Tomita
Keyword(s):  
Compact Group ◽  
Abelian Groups ◽  
Countably Compact ◽  
Convergent Sequences

scholarly journals Abelian torsion groups with a countably compact group topology

2010 ◽  
Vol 157 (1) ◽  
pp. 44-52 ◽  
Author(s):  
Irene Castro-Pereira ◽  
Artur Hideyuki Tomita
Keyword(s):  
Compact Group ◽  
Group Topology ◽  
Countably Compact ◽  
Torsion Groups

scholarly journals Arc components in locally compact groups are Borel sets

2002 ◽  
Vol 65 (1) ◽  
pp. 1-8
Author(s):  
Karl Heinrich Hofmann
Keyword(s):  
Compact Group ◽  
Set Theory ◽  
Abelian Groups ◽  
Affirmative Answer ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Borel Sets ◽  
Models Of Set Theory

Are the arc components in a locally compact group Borel subsets? An affirmative answer is provide for locally compact groups satisfying the First Axiom of Count-ability. For general locally compact groups the question is reduced to compact connected Abelian groups. In certain models of set theory the answer is negative.

scholarly journals Countably compact groups without non-trivial convergent sequences

2020 ◽  
Vol 374 (2) ◽  
pp. 1277-1296 ◽  
Author(s):  
M. Hrušák ◽  
J. van Mill ◽  
U. A. Ramos-García ◽  
S. Shelah
Keyword(s):  
Compact Groups ◽  
Countably Compact ◽  
Convergent Sequences

scholarly journals Lp-improving measures on compact non-abelian groups

1989 ◽  
Vol 46 (3) ◽  
pp. 402-414 ◽  
Author(s):  
Kathryn E. Hare
Keyword(s):  
Compact Group ◽  
Borel Measure ◽  
Abelian Groups ◽  
The Other ◽  
Riesz Product ◽  
Abelian Case ◽  
Compact Abelian Groups

AbstractA Borel measure μ on a compact group G is called Lp-improving if the operator Tμ: L2(G) → L2(G), defined by Tμ(f) = μ * f, maps into Lp(G) for some P > 2. We characterize Lp-improving measures on compact non-abelian groups by the eigenspaces of the operator Tμ if |Tμ|. This result is a generalization of our recent characterization of Lp-improving measures on compact abelian groups.Two examples of Riesz product-like measures are constructed. In contrast with the abelian case one of these is not Lp-improving, while the other is a non-trivial example of an Lp improving measure.

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