Displaying similar documents to “Dimension lowering monotone non-compact mappings of E n ”

On Whitney pairs

Marianna Csörnyei (1999)

Fundamenta Mathematicae

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A simple arc ϕ is said to be a Whitney arc if there exists a non-constant function f such that    l i m x ↦ x 0 ( | f ( x ) - f ( x 0 ) | ) / ( | ϕ ( x ) - ϕ ( x 0 ) | ) = 0 for every x 0 . G. Petruska raised the question whether there exists a simple arc ϕ for which every subarc is a Whitney arc, but for which there is no parametrization satisfying    l i m t ↦ t 0 ( | t - t 0 | ) / ( | ϕ ( t ) - ϕ ( t 0 ) | ) = 0 . We answer this question partially, and study the structural properties of possible monotone, strictly monotone and VBG* functions f and associated Whitney arcs.