Algebraic description of chain transitivity for semigroup actions on flag bundles

In this paper, we introduce the notions of weakly mixing and totally transitivity for a free semigroup action. Let [Formula: see text] be a free semigroup acting on a compact metric space generated by continuous open self-maps. Assuming shadowing for [Formula: see text] we relate the average shadowing property of [Formula: see text] to totally transitivity and its variants. Also, we study some properties such as mixing, shadowing and average shadowing properties, transitivity, chain transitivity, chain mixing and specification property for a free semigroup action.

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Algebraic description of bounded real matrixes

Electronics Letters ◽

10.1049/el:19660392 ◽

1966 ◽

Vol 2 (12) ◽

pp. 464 ◽

Cited By ~ 10

Author(s):

B.D.O. Anderson

Keyword(s):

Algebraic Description

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Homological epimorphisms, homotopy epimorphisms and acyclic maps

Forum Mathematicum ◽

10.1515/forum-2019-0249 ◽

2020 ◽

Vol 32 (6) ◽

pp. 1395-1406

Author(s):

Joseph Chuang ◽

Andrey Lazarev

Keyword(s):

Wide Class ◽

Topological Spaces ◽

Loop Spaces ◽

Graded Algebras ◽

Differential Graded Algebras ◽

Algebraic Description ◽

Acyclic Map ◽

Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

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Joint continuity of affine semigroup actions

Semigroup Forum ◽

10.1007/bf02572546 ◽

1980 ◽

Vol 21 (1) ◽

pp. 153-165 ◽

Cited By ~ 6

Author(s):

Dietrich Helmer

Keyword(s):

Semigroup Actions ◽

Joint Continuity ◽

Affine Semigroup

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Amenability of groupoids arising from partial semigroup actions and topological higher rank graphs

Transactions of the American Mathematical Society ◽

10.1090/tran/6736 ◽

2016 ◽

Vol 369 (4) ◽

pp. 2255-2283 ◽

Cited By ~ 2

Author(s):

Jean N. Renault ◽

Dana P. Williams

Keyword(s):

Semigroup Actions ◽

Higher Rank

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Semigroup actions on ordered groupoids

Mathematica Slovaca ◽

10.2478/s12175-012-0080-3 ◽

2013 ◽

Vol 63 (1) ◽

Author(s):

Niovi Kehayopulu ◽

Michael Tsingelis

Keyword(s):

Commutative Semigroup ◽

Equivalence Relation ◽

Semigroup Actions ◽

Ordered Groupoid ◽

Quasi Order

AbstractIn this paper we prove that if S is a commutative semigroup acting on an ordered groupoid G, then there exists a commutative semigroup S̃ acting on the ordered groupoid G̃:=(G × S)/ρ̄ in such a way that G is embedded in G̃. Moreover, we prove that if a commutative semigroup S acts on an ordered groupoid G, and a commutative semigroup S̄ acts on an ordered groupoid Ḡ in such a way that G is embedded in S̄, then the ordered groupoid G̃ can be also embedded in Ḡ. We denote by ρ̄ the equivalence relation on G × S which is the intersection of the quasi-order ρ (on G × S) and its inverse ρ −1.

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