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Effective regularity criteria for analytic mappings

Adamus J.

Demonstratio Mathematica

2010

Vol. 43, nr 2

235-262

We survey recent developments in the study of singularities of complex-analytic mappings from a local algebraic viewpoint. We present several effective criteria for various modes of regularity of complex-analytic mappings in terms of vertical components in fibred powers of the mappings.

On open mappings of compactifications of the ray onto an arc

Charatonik J. J., Charatonik W. J., Pyrih P.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 1

11-20

The existence of an open mapping from a compactification of a ray onto the closed unit interval [0, 1] is investigated. The main theorem says that such an open mapping does exist if and only if there is a confluent mapping of the remainder onto [0, 1].

Path-lifting property for 0-dimensional confluent mappings

Krasinkiewicz J.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 4

357-367

We prove a stronger version of the classical theorem of Whyburn on the liftings of dendrites relative to 0-dimensional open mappings of compact metric spaces.