Confluent Mappings and Arc Kelley Continua

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, then X itself is a(n) (arc) Kelley continuum. In particular each confluently LC-representable continuum is arc Kelley. It is also proved that if continua X and Y are confluently LC-representable, then also are their product X x Y and the hyperspaces 2^x and C(X).