The shift on the inverse limit of a covering projection

1987 ◽  
Vol 59 (2) ◽  
pp. 129-149 ◽  
Author(s):  
Cem Tezer
Keyword(s):  
Inverse Limit ◽  
Covering Projection

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Generating the inverse limit of free groups

2021 ◽  
Vol 578 ◽  
pp. 371-401
Author(s):  
Gregory R. Conner ◽  
Wolfgang Herfort ◽  
Curtis A. Kent ◽  
Petar Pavešić
Keyword(s):  
Inverse Limit ◽  
Free Groups

scholarly journals A characterization of a map whose inverse limit is an arc

2021 ◽  
pp. 1-17
Author(s):  
SINA GREENWOOD ◽  
SONJA ŠTIMAC
Keyword(s):  
Continuous Function ◽  
Inverse Limit ◽  
Splitting Sequence

Abstract For a continuous function $f:[0,1] \to [0,1]$ we define a splitting sequence admitted by f and show that the inverse limit of f is an arc if and only if f does not admit a splitting sequence.

Invariants of weak equivalence in primitive matrices

2000 ◽  
Vol 20 (2) ◽  
pp. 611-626 ◽  
Author(s):  
RICHARD SWANSON ◽  
HANS VOLKMER
Keyword(s):  
Inverse Limit ◽  
Direct Application ◽  
Topological Classification ◽  
Weak Equivalence ◽  
Transition Matrices ◽  
Inverse Limit Spaces ◽  
Positive Dimension ◽  
One Dimensional ◽  
Dimension Group

Weak equivalence of primitive matrices is a known invariant arising naturally from the study of inverse limit spaces. Several new invariants for weak equivalence are described. It is proved that a positive dimension group isomorphism is a complete invariant for weak equivalence. For the transition matrices corresponding to periodic kneading sequences, the discriminant is proved to be an invariant when the characteristic polynomial is irreducible. The results have direct application to the topological classification of one-dimensional inverse limit spaces.

scholarly journals Characterisation of polyhedral products with finite generalised Postnikov decomposition

2020 ◽  
Vol 32 (5) ◽  
pp. 1253-1269
Author(s):  
Kouyemon Iriye ◽  
Daisuke Kishimoto ◽  
Ran Levi
Keyword(s):  
Finite Length ◽  
Inverse Limit ◽  
Universal Cover ◽  
Homotopy Equivalent ◽  
Polyhedral Product ◽  
Postnikov Tower

AbstractA generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product {Z_{K}(X,A)} whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower. We also include p-local and rational versions of the theorem. We end with a group theoretic application.

Profinite Modules

1973 ◽  
Vol 16 (3) ◽  
pp. 405-415
Author(s):  
Gerard Elie Cohen
Keyword(s):  
Finite Group ◽  
General Theory ◽  
Finite Length ◽  
Finite Groups ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Point Of View ◽  
Inverse Limits ◽  
Profinite Groups ◽  
Inverse Systems

An inverse limit of finite groups has been called in the literature a pro-finite group and we have extensive studies of profinite groups from the cohomological point of view by J. P. Serre. The general theory of non-abelian modules has not yet been developed and therefore we consider a generalization of profinite abelian groups. We study inverse systems of discrete finite length R-modules. Profinite modules are inverse limits of discrete finite length R-modules with the inverse limit topology.

scholarly journals The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

2022 ◽  
Vol 2022 ◽  
pp. 1-6
Author(s):  
Zhan jiang Ji
Keyword(s):  
Inverse Limit ◽  
Point Sets ◽  
Recurrent Point ◽  
Shadowing Property ◽  
Limit Space ◽  
Shift Map ◽  
Dynamical Properties ◽  
Definition Of ◽  
Inverse Limit Space

According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their dynamical properties. The following results are obtained: (1) Regularly recurrent point sets of the double shift map σ f ∘ σ g are equal to the double inverse limit space of the double self-map f ∘ g in the regularly recurrent point sets. (2) The double self-map f ∘ g has sequence shadowing property if and only if the double shift map σ f ∘ σ g has sequence shadowing property. Thus, the conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space.

scholarly journals Sensitivity for topologically double ergodic dynamical systems

2021 ◽  
Vol 6 (10) ◽  
pp. 10495-10505
Author(s):  
Risong Li ◽  
◽  
Xiaofang Yang ◽  
Yongxi Jiang ◽  
Tianxiu Lu ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Metric Space ◽  
Inverse Limit ◽  
Compact Metric Space ◽  
Limit Space ◽  
Factor Map ◽  
Continuous Surjection ◽  
Inverse Limit Space

<abstract><p>As a stronger form of multi-sensitivity, the notion of ergodic multi-sensitivity (resp. strongly ergodically multi-sensitivity) is introduced. In particularly, it is proved that every topologically double ergodic continuous selfmap (resp. topologically double strongly ergodic selfmap) on a compact metric space is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive). And for any given integer $ m\geq 2 $, $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ f^{m} $. Also, it is shown that if $ f $ is a continuous surjection, then $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ \sigma_{f} $, where $ \sigma_{f} $ is the shift selfmap on the inverse limit space $ \lim\limits_{\leftarrow}(X, f) $. Moreover, it is proved that if $ f:X\rightarrow X $ (resp. $ g:Y\rightarrow Y $) is a map on a nontrivial metric space $ (X, d) $ (resp. $ (Y, d') $), and $ \pi $ is a semiopen factor map between $ (X, f) $ and $ (Y, g) $, then the ergodic multi-sensitivity (resp. the strongly ergodic multi-sensitivity) of $ g $ implies the same property of $ f $.</p></abstract>

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