Dynamical notions along filters

zbMath1527.37005arXiv2204.01344MaRDI QIDQ6179149

Lorenzo Luperi Baglini, Sourav Kanti Patra, Md. Moid Shaikh

Publication date: 5 September 2023

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.01344

zbMATH Keywords

dynamical systemStone-Čech compactificationproximalityuniform recurrence

Mathematics Subject Classification ID

Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) ?ech types (55N05) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Cites Work

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• Algebra in the Stone-Čech compactification. Theory and applications
• The semigroup of ultrafilters near an idempotent of a semitopological semigroup
• Filters and semigroup properties
• Topological dynamics and combinatorial number theory
• The semigroup of ultrafilters near 0
• Ramsey properties of nonlinear Diophantine equations
• Dynamical characterizations of combinatorially rich sets near zero
• The minimal ideal of compact subsemigroups of \(\beta S\)
• Central sets and their combinatorial characterization
• Partition regularity of polynomial systems near zero
• Dynamical characterization of central sets along filter
• Algebraic characterizations of some relative notions of size
• Central sets theorem along filters and some combinatorial consequences
• Combined algebraic properties of \(C^\ast\)-sets near zero
• Dynamics near an idempotent
• The closure of the smallest ideal of an ultrafilter semigroup
• Dynamical characterization of C-sets and its application
• Nonmetrizable topological dynamical characterization of central sets
• Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
• Monochromatic sums equal to products near zero
• Nonmetrizable Topological Dynamics and Ramsey Theory
• A new and stronger central sets theorem
• Partition Regularity of Nonlinear Polynomials: a Nonstandard Approach
• Central sets theorem near zero

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