Abstract
To any continuum X weassign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application weconstruct an uncountable family of metric continua X homeomorphic to C(X).
Recommended Citation
J. J. Charatonik and W. J. Charatonik, "A Degree of Nonlocal Connectedness," Rocky Mountain Journal of Mathematics, Rocky Mountain Mathematics Consortium, Jan 2001.
The definitive version is available at https://doi.org/10.1216/rmjm/1021249438
Department(s)
Mathematics and Statistics
Keywords and Phrases
Cartesian Product; Continuum; Degree; Hereditarily Unicoherent; Inverse Limit; Locally Connected; Ordinal Number; Hyperspace
International Standard Serial Number (ISSN)
0035-7596
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2001 Rocky Mountain Mathematics Consortium, All rights reserved.
Publication Date
01 Jan 2001
