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On Suslinian Continua

Published online by Cambridge University Press:  20 November 2018

D. Daniel ,
J. Nikiel ,
L. B. Treybig ,
H. M. Tuncali  and
E. D. Tymchatyn
D. Daniel
Affiliation:
Lamar University, Department of Mathematics, Beaumont, TX 77710, U.S.A. e-mail: daniel@math.lamar.edu
J. Nikiel
Affiliation:
American University of Beirut, Department of Mathematics, Beirut, Lebanon e-mail: nikiel@aub.edu.lb
L. B. Treybig
Affiliation:
Texas A&M University, Department of Mathematics, College Station, TX 77843, U.S.A. e-mail: treybig@math.tamu.edu
H. M. Tuncali
Affiliation:
Nipissing University, Faculty of Arts and Sciences, North Bay, ON, P1B 8L7 e-mail: muratt@topology.nipissingu.ca
E. D. Tymchatyn
Affiliation:
University of Saskatchewan, Department of Mathematics, Saskatoon, SK, S7N 0W0 e-mail: tymchat@snoopy.usask.ca
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Abstract

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A continuumis 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 atmost ${{\omega }_{1}}$ and under appropriate set-theoretic conditions are metrizable. Non-separable locally connected Suslinian continua are rim-finite on some open set.

Keywords

54F1554D1554F50Suslinian continuumSouslin linelocally connectedrim-metrizableperfectly normalrim-finite
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 195 - 202
Copyright
Copyright © Canadian Mathematical Society 2005

References

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