Open Access. Powered by Scholars. Published by Universities.®
![Digital Commons Network](http://assets.bepress.com/20200205/img/dcn/DCsunburst.png)
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
A Degree Of Nonlocal Connectedness, J. J. Charatonik, W. J. Charatonik
A Degree Of Nonlocal Connectedness, J. J. Charatonik, W. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
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).