Glasnik Matematicki, Vol. 37, No.2 (2002), 375-382.

THE PROPERTY RNT ON DENDROIDS

Veronica Martinez-de-la-Vega

Abstract.   A continuum is said to be retractable onto near trees (abbreviating RNT) provided that for each ε > 0 there exists δ > 0 such that if T is a tree in X and H(T,X) < δ, then there exists an ε-retraction r of X onto T. In this paper it is proved that an arcwise connected continuum with the property RNT is a dendroid. We focus our study on dendroids. Dendrites are characterized as: (a) smooth dendroids with property RNT, (b) dendroids with the property RNT hereditarily. Finally, an example of a nonlocally connected dendroid with property RNT is shown.

2000 Mathematics Subject Classification.   54F15, 54F50, 54F65, 54C15.

Key words and phrases.   Continuum, dendrite, dendroid, retraction, tree.