Inverse Limit of an Inverse System of BE-algebras

AbstractIn proving the contractibility of certain hyperspaces J. L. Kelley identified and defined a certain uniformnessproperty which he called Property 3.2. It is known that the classes of locally connected continua, homogeneous continua and hereditarily indecomposable continua have Property 3.2. In this paper we prove that two examples of indecomposable continua developed respectively by the authors have Property 3.2. One is the example of a nonchainable atriodic tree-like continuum with positive span which was defined by the first author, and the other is a nonchainable, noncircle-like continuum which has the cone=hyperspace property which was defined by the second author. Each of the examples is an inverse limit of an inverse system having a single bonding map.

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A Note on Inverse Limits of Finite Spaces

Canadian Mathematical Bulletin ◽

10.4153/cmb-1970-014-7 ◽

1970 ◽

Vol 13 (1) ◽

pp. 69-70

Author(s):

S. B. Nadler

Keyword(s):

Finite Groups ◽

Inverse Limit ◽

Inverse System ◽

Inverse Limits ◽

Hausdorff Spaces ◽

Finite Spaces

The following lemma, which appears as Lemma 4 in [5], was used to determine certain multicoherence properties of inverse limits of continua.Lemma. Let X denote the inverse limit of an inverse system {Xλ, fλμ, Λ} of compact Hausdorff spaces Xλ. If Xλ has no more than k components (where k < ∞ is fixed) for each λ ∊ Λ, then X has no more than k components.In this paper we give a set theoretic analogue of this lemma and an extension which was suggested to the author by Professor F. W. Lawvere. An application to inverse limits of finite groups is then given.

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The spectrum (P ⋀ bo) −∞

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410006196x ◽

1984 ◽

Vol 96 (1) ◽

pp. 85-93 ◽

Cited By ~ 7

Author(s):

Donald M. Davis ◽

Mark Mahowald

Keyword(s):

Inverse Limit ◽

Projective Spaces ◽

Inverse System ◽

Cohomology Groups ◽

Image Position ◽

Adic Completion

There are spectra P−k constructed from stunted real projective spaces as in [1] such that H*(P−k) is the span in ℤ/2[x, x−1] of those xi with i ≥ −k. (All cohomology groups have ℤ/2-coefficients unless specified otherwise.) Using collapsing maps, these form an inverse systemwhich is similar to those of Lin ([15], p. 451). It is a corollary of Lin's work that there is an equivalence of spectrawhere holim is the homotopy inverse limit ([3], ch. 5) and Ŝ–1 the 2-adic completion of a sphere spectrum. One may denote by this holim (P–κ), although one must constantly keep in mind that , but rather

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Inverse limits of finite rank free groups

Journal of Group Theory ◽

10.1515/jgt-2012-0019 ◽

2012 ◽

Vol 15 (6) ◽

Cited By ~ 1

Author(s):

Gregory R. Conner ◽

Curtis Kent

Keyword(s):

Homomorphic Image ◽

Free Group ◽

Finite Rank ◽

Inverse Limit ◽

Free Groups ◽

Inverse System ◽

Inverse Limits ◽

Universal Group ◽

Hawaiian Earring ◽

Constant System

Abstract.We will show that the inverse limit of finite rank free groups with surjective connecting homomorphism is isomorphic either to a finite rank free group or to a fixed universal group. In other words, any inverse system of finite rank free groups which is not equivalent to an eventually constant system has the universal group as its limit. This universal inverse limit is naturally isomorphic to the first shape group of the Hawaiian earring. We also give an example of a homomorphic image of the Hawaiian earring group which lies in the inverse limit of free groups but is neither a free group nor isomorphic to the Hawaiian earring group.

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Topological n-cells and Hilbert cubes in inverse limits

Applied General Topology ◽

10.4995/agt.2018.7061 ◽

2018 ◽

Vol 19 (1) ◽

pp. 9

Author(s):

Leonard R. Rubin

Keyword(s):

Set Theory ◽

Weak Topology ◽

Inverse Limit ◽

Metrizable Space ◽

Inverse System ◽

Inverse Limits ◽

Hilbert Cube ◽

Compact Metrizable Space ◽

Metric Topology

It has been shown by S. Mardešić that if a compact metrizable space X has dim X ≥ 1 and X is the inverse limit of an inverse sequence of compact triangulated polyhedra with simplicial bonding maps, then X must contain an arc. We are going to prove that if X = (|Ka|,pba,(A,)<a href="http://www.codecogs.com/eqnedit.php?latex=\preceq" target="_blank"><img title="\preceq" src="http://latex.codecogs.com/gif.latex?\preceq" alt="" /></a>)is an inverse system in set theory of triangulated polyhedra|Ka|with simplicial bonding functions pba and X = lim X, then there exists a uniquely determined sub-inverse system XX= (|La|, pba|Lb|,(A,<a href="http://www.codecogs.com/eqnedit.php?latex=\preceq" target="_blank"><img title="\preceq" src="http://latex.codecogs.com/gif.latex?\preceq" alt="" /></a>)) of X where for each a, La is a subcomplex of Ka, each pba|Lb|:|Lb| → |La| is surjective, and lim XX = X. We shall use this to generalize the Mardešić result by characterizing when the inverse limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps must contain a topological n-cell and do the same in the case of an inverse system of finite triangulated polyhedra with simplicial bonding maps. We shall also characterize when the inverse limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps must contain an embedded copy of the Hilbert cube. In each of the above settings, all the polyhedra have the weak topology or all have the metric topology(these topologies being identical when the polyhedra are finite).

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Inverse System in The Category of Intuitionistic Fuzzy Soft Modules

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v14i1.7123 ◽

2018 ◽

Vol 14 (1) ◽

pp. 7486-7502

Author(s):

S. E. Abdullayev ◽

Sadi Bayramov

Keyword(s):

Exact Sequence ◽

Inverse Limit ◽

Inverse System ◽

Derived Functor ◽

Intuitionistic Fuzzy ◽

Homology Algebra ◽

Basic Concepts ◽

Exact Sequences

This paper begins with the basic concepts of soft module. Later, we introduce inverse system in the category of intutionistic fuzzy soft modules and prove that its limit exists in this category. Generally, limit of inverse system of exact sequences of intutionistic fuzzy soft modules is not exact. Then we define the notion which is first derived functor of the inverse limit functor. Finally, using methods of homology algebra, we prove that the inverse system limit of exact sequence of intutionistic fuzzy soft modules is exact.

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The existence of an inverse limit of an inverse system of measure spaces — A purely measurable case

Acta Mathematica Hungarica ◽

10.1007/s10474-009-8248-1 ◽

2009 ◽

Vol 126 (1-2) ◽

pp. 65-77 ◽

Cited By ~ 1

Author(s):

M. Pintér

Keyword(s):

Inverse Limit ◽

Inverse System ◽

Measure Spaces

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Diagonal forms of higher degree over function fields of p-adic curves

International Journal of Number Theory ◽

10.1142/s1793042120500098 ◽

2019 ◽

Vol 16 (01) ◽

pp. 161-172

Author(s):

S. Pumplün

Keyword(s):

Function Field ◽

Inverse Limit ◽

Function Fields ◽

Inverse System ◽

Diagonal Forms ◽

Forms Of Higher Degree

We investigate diagonal forms of degree [Formula: see text] over the function field [Formula: see text] of a smooth projective [Formula: see text]-adic curve: if a form is isotropic over the completion of [Formula: see text] with respect to each discrete valuation of [Formula: see text], then it is isotropic over certain fields [Formula: see text], [Formula: see text] and [Formula: see text]. These fields appear naturally when applying the methodology of patching; [Formula: see text] is the inverse limit of the finite inverse system of fields [Formula: see text]. Our observations complement some known bounds on the higher [Formula: see text]-invariant of diagonal forms of degree [Formula: see text]. We only consider diagonal forms of degree [Formula: see text] over fields of characteristic not dividing [Formula: see text].

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A closer look at the stable completion

10.23943/princeton/9780691161686.003.0005 ◽

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.

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Inductor Saturation Compensation in Three-Phase Three-Wire Voltage-Source Converters via Inverse System Dynamics-I

10.36227/techrxiv.12378371 ◽

2020 ◽

Author(s):

Ziya Özkan ◽

Ahmet Masum Hava

Keyword(s):

Dynamic Model ◽

Dynamic Performance ◽

Current Control ◽

Inverse System ◽

Voltage Source ◽

Voltage Source Converter ◽

Two Phase ◽

Inverse Dynamic ◽

Three Phase ◽

Steady State Current

In three-phase three-wire (3P3W) voltage-source converter (VSC) systems, utilization of filter inductors with deep saturation characteristics is often advantageous due to the improved size, cost, and efficiency. However, with the use of conventional synchronous frame current control (CSCC) methods, the inductor saturation results in significant dynamic performance loss and poor steady-state current waveform quality. This paper proposes an inverse dynamic model based compensation (IDMBC) method to overcome these performance issues. Accordingly, a review of inductor saturation and core materials is performed, and the motivation on the use of saturable inductors is clarified. Then, two-phase exact modelling of the 3P3W VSC control system is obtained and the drawbacks of CSCC have been demonstrated analytically. Based on the exact modelling, the inverse system dynamic model of the nonlinear system is obtained and employed such that the nonlinear plant is converted to a fictitious linear inductor system for linear current regulators to perform satisfactorily.

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