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APOTP FOR THE INVERSE LIMIT SPACES 被引量:9
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作者 Gu Rongbao Sheng Yeqing 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期473-478,共6页
The connection between APOTP (asymptotic pseudo orbit tracing property) for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is ... The connection between APOTP (asymptotic pseudo orbit tracing property) for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP. 展开更多
关键词 APOTP inverse limit space shift map pseudoarc.
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Inverse limits of hereditarily almost expandable class
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作者 ZHAO Bin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第2期237-244,共8页
In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system (Xα, π^αβ, ∧}. (1) Suppose X is heredita... In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system (Xα, π^αβ, ∧}. (1) Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal (almost θ-expandable, almost discrete θ-expandable), then so is X; (2) Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable (almost discrete σ-expandable = σ-pointwise collectionwise normal), then so is X. 展开更多
关键词 inverse limit space κ-metacompactness κ-σ-metacompactness hereditarily pointwise collection- wise normal hereditarily almost θ-expandable hereditarily almost σ-expandable
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B(LF,ω~2 )-refinability of inverse limits
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作者 XIONG Zhao-hui YANG Ming-quan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第4期496-502,共7页
Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα : X → Xα is an open and onto map and X is A-paracompact. We prove that if each ... Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα : X → Xα is an open and onto map and X is A-paracompact. We prove that if each Xα is B(LF, ω^2)-refinable (hereditarily B(LF, ω^2)- refinable), then X is B(LF, ω^2)-refinable (hereditarily B(LF,ω ^2)-refinable). Furthermore, we show that B(LF, ω^2)-refinable spaces can be preserved inversely undcr closed maps. 展开更多
关键词 inverse limit B(LF ω^2)-refinability hereditary B(LF ω ^2)-refinability.
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On Inverse Limits of Normal δθ-refinable Spaces
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作者 CAO Jin-wen (College of Information Management, Chengdu University of Technol ogy, Chengdu 610059, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第3期286-290,共5页
This paper proves the following results: Le t X= lim ←{X σ,π σ ρ,Λ},|Λ|=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-ref... This paper proves the following results: Le t X= lim ←{X σ,π σ ρ,Λ},|Λ|=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable . 展开更多
关键词 inverse limit Λ-PARACOMPACT normal and δθ -refinable hereditarily normal hereditarily δθ-refinable.
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Inverse Limit of Spaces of Upper Semicontinuous Functions
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作者 张德学 《Northeastern Mathematical Journal》 CSCD 2001年第1期49-52,共4页
Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor o... Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor on compact Hausdorff space. It is proved in this note that this functor preserves inverse limits. 展开更多
关键词 upper semicontinuous function continuous lattice lim inf convergence inverse limit
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An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1] 被引量:2
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作者 HongMO SongQuanSHI +1 位作者 FangPingZENG JieHuaMAI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第5期925-932,共8页
Let I=[0,1],c_1,c_2 ∈(0,1)with c_1<c_2 and f:I→I be a continuous map satisfying:f|_[0,c_1] and f|_[c_2,1] are both strictly increasing and f|_[c_1,c_2]is strictly decreasing.Let A ={z ∈[0,c_1]|f(x)=x}, a=maxA,a_... Let I=[0,1],c_1,c_2 ∈(0,1)with c_1<c_2 and f:I→I be a continuous map satisfying:f|_[0,c_1] and f|_[c_2,1] are both strictly increasing and f|_[c_1,c_2]is strictly decreasing.Let A ={z ∈[0,c_1]|f(x)=x}, a=maxA,a_1=max(A\{a}),and B={x∈[c_2,1]|f(x)=x},b=minB,b_1=min(B\{b}).Then the in- verse limit(I,f)is an arc if and only if one of the following three conditions holds: (1)If c_1<f(c_1)≤c_2(resp.c_1≤f(c_2)<c_2),then f has a single fixed point,a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods,furthermore,if A≠φ and B≠φ,then f(c2)>a(resp.f(c_1)<b). (2)If f(c_1)≤c_1(resp.f(c_2)≥c_2),then f has more than one fixed point,furthermore,if B≠φ and A\{a}≠φ,f(c_2)≥a or if a_1<f(c_2)<a,f^2(c_2)>f(c_2),(resp.f has more than one fixed point,furthermore,if A≠φ and B\{b}≠φ,f(c_1)≤b or if b<f(c_2)<b_1,f^2(c_1)<f(c_1)). (3)If f(c_1)>c_2 and f(c_2)<c_1,then f has a single fixed point,a single period two orbit lying in I\(u,v)but no points of period greater than two,where u,v ∈[c_1,c_2] such that f(u)=c_2 and f(v)=c_1. 展开更多
关键词 inverse limit ARC Uninmodel map Periodic point
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Inverse Limits in Representations of a Restricted Lie Algebra
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作者 Yu Feng YAO Bin SHU Yi Yang LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第12期2463-2474,共12页
Let (g, [p]) be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of "higher" reduced enveloping algebras {uxs (g) I s ∈ N} with X running over g* ma... Let (g, [p]) be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of "higher" reduced enveloping algebras {uxs (g) I s ∈ N} with X running over g* make representations of g split into different "blocks". In this paper, we study such an infinite- dimensional algebra Ax (g) :=lim Uxs (g) for a given X C g*. A module category equivalence is built between subcategories of U(g)-rnod and Ax(g)-mod. In the case of reductive Lie algebras, (quasi) generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized x-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity. 展开更多
关键词 Restricted Lie algebra reductive Lie algebra inverse limit projective module standard Levi form
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CHAOS AND ORDER OF INVERSE LIMIT SPACE FOR A GRAPH MAP
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作者 LUJIE 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2000年第1期25-32,共8页
With the method of inverse limit, the author obtains several criteria of chaos of piecewise monotone continuous maps on finite graphs.
关键词 CHAOS inverse limit Order Recurrent point
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Meta-projective Modules, Tensor Products and Limits 被引量:2
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作者 冯良贵 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第1期61-64, ,共4页
In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a suf... In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a sufficient condition for lgldim (R1 R2,)≥lgldim R1+lgldimR2, and wgldim (R1 R2) ≥wgldimR1 +wgldimR2 展开更多
关键词 inverse limit tensor product meta-projective modules meta-injective modules
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On Some Questions of Barge and Toledo 被引量:1
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作者 牛应轩 叶向东 《Northeastern Mathematical Journal》 CSCD 2000年第4期439-444,共6页
Barge asked if each homeomorphism of a hereditarily decomposable chainable continuum has zero topological entropy and Toledo asked if a homeomorphism of a chainable continuum can always be induced by square commuting ... Barge asked if each homeomorphism of a hereditarily decomposable chainable continuum has zero topological entropy and Toledo asked if a homeomorphism of a chainable continuum can always be induced by square commuting diagram on inverse systems of finite graphs. We show in this note that if Toledos question has a positive answer then Barges question also has a positive answer. 展开更多
关键词 topological entropy inverse limit space induced map and homeomorphism
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Representations of Free Groups on Rational Line Q
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作者 Bing-xin Lu Zuo-tong Zhu 《Advances in Manufacturing》 2000年第2期101-105,共5页
A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of count... A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications,we obtain the highly ordered transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q. 展开更多
关键词 free group highly ordered transitive representation direct product of groups inverse limit of free groups
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Hereditarily covering properties of inverse sequence limits
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作者 Bin ZHAO Aili SONG Jing WEI 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第4期987-997,共11页
Let {Xi,πki,ω} be an inverse sequence and X -- lim{Xi,πki,ω). If each Xi is hereditarily (resp. metaLindelSf, σ-metaLindelSf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly... Let {Xi,πki,ω} be an inverse sequence and X -- lim{Xi,πki,ω). If each Xi is hereditarily (resp. metaLindelSf, σ-metaLindelSf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly δθ-refinable), then so is X. 展开更多
关键词 inverse sequence limit hereditarily metaLindelofness hereditarily weakly suborthocompactness hereditarily δθ-refinability hereditarily weakly θ-refinability countable product
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Entropy,Periodicity,and Graphs with Zero Euler Characteristic 被引量:3
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作者 JieLU JinChengXIONG JianCHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第3期415-422,共8页
Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,... Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G. 展开更多
关键词 GRAPH Topological entropy inverse limit PERIOD
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