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).
W. J. Charatonik et al., "Confluent Mappings and Arc Kelley Continua," Rocky Mountain Journal of Mathematics, Rocky Mountain Math Consortium, Jul 2008.
The definitive version is available at https://doi.org/10.1216/RMJ-2008-38-4-1091
Mathematics and Statistics
Keywords and Phrases
Arc Kelley continuum; Knaster type continuum; confluent mapping; continuum; inverse limit; locally connected; monotone; solenoid
Article - Journal
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