Glasnik Matematicki, Vol. 48, No. 2 (2013), 429-442.

ON STRONGLY FREELY DECOMPOSABLE AND INDUCED MAPS

Javier Camargo and Sergio Macias

Escuela de Matemáticas, Facultad de Ciencias, Universidad Industrial de Santander, Ciudad Universitaria, Carrera 27 Calle 9, Bucaramanga, Santander, A. A. 678, Colombia
e-mail: jcam@matematicas.uis.edu.co

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D. F., C. P. 04510, Mexico
e-mail: sergiom@matem.unam.mx

Abstract.   Freely decomposable and strongly freely decomposable maps were introduced by G. R. Gordh and C. B. Hughes as a generalization of monotone maps with the property that these maps preserve local connectedness in inverse limits. We prove some relationships between f, Cn(f) and 2f, when f, Cn(f) or 2f belong to the following classes of maps: Almost monotone, quasi-monotone, weakly monotone, freely decomposable or strongly freely decomposable. We correct two corollaries formulated by Jaunusz J. Charatonik in ``On feebly monotone and related classes of maps''. We also present an alternative reformulation of these results.

2010 Mathematics Subject Classification.   54B20, 54E40, 54F15.

Key words and phrases.   Confluent map, continua, freely decomposable map, irreducible continuum, local homeomorphism, monotone map, quasi-monotone map, strongly freely decomposable map.

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DOI: 10.3336/gm.48.2.14

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