Mathematics Commons^™

Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A Kelley continuum X, also called a continuum with the property of Kelley, such that, for each p X, each subcontinuum K containing p is approximated by arc-wise connected continua containing p, is called an arc Kelley continuum. A continuum homeomorphic to the inverse limit of locally connected continua with confluent bonding maps is said to be confluently LC-representable. The main subject of the paper is a study of deep connections between the arc Kelley continua and confluent mappings. It is shown that if a continuum X admits, for each ε > 0, a confluent ε-mapping onto a(n) (arc) Kelley continuum, …