Search results for "Baire"

showing 3 items of 13 documents

Homogeneous actions on the random graph

2018

We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite.

Random graphFinite group20B22 (primary) 20E06 20E05 05C63 54E52 (secondary)Group Theory (math.GR)Homogeneous actions16. Peace & justicegroups acting on trees[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Action (physics)CombinatoricsMathematics::Group TheoryFree productHomogeneousBaire category theoremFOS: MathematicsDiscrete Mathematics and CombinatoricsCountable setBaire category theoremfree groupsGeometry and TopologyFinitely-generated abelian groupMathematics - Group TheoryMSC: 20B22 (primary); 20E06 20E05 05C63 54E52 (secondary)random graphMathematicsGroups, Geometry, and Dynamics
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Highly transitive actions of free products

2013

We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group $\PSL_2(\Z)\simeq (\Z/2\Z)*(\Z/3\Z)$ admits a faithful and highly transitive action on a countable set.

Transitive actionHighly transitive actionsMSC: Primary: 20B22 20E06Group Theory (math.GR)01 natural sciencesBaire category Theorem[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsFree products0103 physical sciencesFOS: MathematicsCountable set0101 mathematics20B22MathematicsTransitive relation20E06Group (mathematics)Mathematics::Operator Algebras010102 general mathematics20E06 20B2216. Peace & justiceFree productBaire category theorem010307 mathematical physicsGeometry and TopologyMathematics - Group Theory
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MR3157399 Reviewed: Kesavan, S. Continuous functions that are nowhere differentiable. Math. Newsl. 24 (2013), no. 3, 49–52. (54C05)

2014

The author uses the Baire category theorem to prove the existence of nowhere differentiable functions in C([0,1]). Precisely, the author proves the following: Theorem 1. There exist continuous functions on the interval [0,1] which are nowhere differentiable. In fact, the collection of all such functions forms a dense subset of C([0,1]).

nowhere differentiable functiondense subsetSettore MAT/05 - Analisi MatematicaBaire category
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