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On Suslinian Continua

  Published:2005-06-01
 Printed: Jun 2005
  • D. Daniel
  • J. Nikiel
  • L. B. Treybig
  • H. M. Tuncali
  • E. D. Tymchatyn
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Abstract

A continuum is said to be Suslinian if it does not contain uncountably many mutually exclusive nondegenerate subcontinua. We prove that Suslinian continua are perfectly normal and rim-metrizable. Locally connected Suslinian continua have weight at most $\omega_1$ and under appropriate set-theoretic conditions are metrizable. Non-separable locally connected Suslinian continua are rim-finite on some open set.
Keywords: Suslinian continuum, Souslin line, locally connected, rim-metrizable, perfectly normal, rim-finite Suslinian continuum, Souslin line, locally connected, rim-metrizable, perfectly normal, rim-finite
MSC Classifications: 54F15, 54D15, 54F50 show english descriptions Continua and generalizations
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
54F15 - Continua and generalizations
54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54F50 - Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
 

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