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<p>In this paper, we find uncountable families of generalized inverse sequences on intervals, where the bonding functions consist of a finite number of line segments, such that the inverse limit spaces of these sequences are pointwise self-homeomorphic continua. We give several examples of pointwise self-homeomorphic continua obtained in this manner including the dendrite <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(D_3\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> and a dendrite containing <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(D_\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>ω</mi> </msub> </math></EquationSource> </InlineEquation>. The dendrite <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(D_3\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> was obtained previously, by others, as a generalized inverse limit but the bonding function in that example contained infinitely many line segments. We show that the techniques we use on intervals can be extended to inverse limits where the factor spaces are finite trees to again obtain pointwise self-homeomorphic continua.</p>

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Pointwise self-homeomorphic generalized inverse limits

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Ali H. Ali,
  • Faruq A. Mena,
  • Robert P. Roe

摘要

In this paper, we find uncountable families of generalized inverse sequences on intervals, where the bonding functions consist of a finite number of line segments, such that the inverse limit spaces of these sequences are pointwise self-homeomorphic continua. We give several examples of pointwise self-homeomorphic continua obtained in this manner including the dendrite \(D_3\) D 3 and a dendrite containing \(D_\omega \) D ω . The dendrite \(D_3\) D 3 was obtained previously, by others, as a generalized inverse limit but the bonding function in that example contained infinitely many line segments. We show that the techniques we use on intervals can be extended to inverse limits where the factor spaces are finite trees to again obtain pointwise self-homeomorphic continua.