Glasnik Matematicki, Vol. 37, No.2 (2002), 375-382.
THE PROPERTY RNT ON DENDROIDS
Instituto de Matematicas, UNAM,
Circuito Exterior, Cd. Universitaria,
Mexico, 04510, D.F., Mexico
Abstract. A continuum is said to be
retractable onto near trees (abbreviating RNT)
provided that for each
ε > 0
δ > 0
such that if T is a
tree in X and H(T,X) <
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
2000 Mathematics Subject Classification.
54F15, 54F50, 54F65, 54C15.
Key words and phrases. Continuum, dendrite, dendroid,
Full text (PDF) (free access)
Glasnik Matematicki Home Page