Original scientific paper

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 > 0 there exists > 0 such that if T is a tree in X and H(T,X) < , then there exists an -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.

Keywords

Continuum; dendrite; dendroid; retraction; tree

Hrčak ID:

4805

URI

https://hrcak.srce.hr/4805

Publication date:

1.12.2002.

Visits: 865 *